%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM924+7 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 : Sat Jun 21 05:22:23 AM UTC 2025
% Result : Theorem 248.21s 248.54s
% Output : Proof 248.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 68
% Syntax : Number of formulae : 173 ( 67 unt; 0 typ; 0 def)
% Number of atoms : 598 ( 278 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 668 ( 263 ~; 248 |; 12 &)
% ( 125 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-4 aty)
% Number of variables : 275 ( 252 !; 0 ?; 275 :)
% Comments :
%------------------------------------------------------------------------------
tff(zero_zero_type,type,
zero_zero: $i > $i ).
tff(int_type,type,
int: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i * $i * $i ) > $i ).
tff(number_number_of_type,type,
number_number_of: ( $i * $i ) > $i ).
tff(bit0_type,type,
bit0: $i > $i ).
tff(bit1_type,type,
bit1: $i > $i ).
tff(pls_type,type,
pls: $i ).
tff(nat_type,type,
nat: $i ).
tff(power_power_type,type,
power_power: ( $i * $i ) > $i ).
tff(plus_plus_type,type,
plus_plus: ( $i * $i ) > $i ).
tff(s_type,type,
s: $i ).
tff(ti_type,type,
ti: ( $i * $i ) > $i ).
tff(t_type,type,
t: $i ).
tff(times_times_type,type,
times_times: ( $i * $i ) > $i ).
tff(one_one_type,type,
one_one: $i > $i ).
tff(m_type,type,
m: $i ).
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(semiring_1_type,type,
semiring_1: $i > $o ).
tff(linordered_idom_type,type,
linordered_idom: $i > $o ).
tff(number_type,type,
number: $i > $o ).
tff(1,plain,
( ( pls = zero_zero(int) )
<=> ( pls = zero_zero(int) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Pls__def) ).
tff(3,plain,
pls = zero_zero(int),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( ti(int,pls) = pls )
<=> ( ti(int,pls) = pls ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
ti(int,pls) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
tff(6,plain,
ti(int,pls) = pls,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
zero_zero(int) = pls,
inference(symmetry,[status(thm)],[3]) ).
tff(8,plain,
hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)) = hAPP(int,fun(int,bool),ord_less(int),pls),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
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(pls))))),m)),one_one(int))),t)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,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(pls))))),m)),one_one(int))),t)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,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(pls))))),m)),one_one(int))),t)))
<=> ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,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(13,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)],[12]) ).
tff(14,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(15,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/sandbox/benchmark/theBenchmark.p',fact_79_int__one__le__iff__zero__less) ).
tff(16,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)],[15,14]) ).
tff(17,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)],[16]) ).
tff(18,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)],[17,13]) ).
tff(19,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(20,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)],[19,18]) ).
tff(21,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(22,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096) ).
tff(23,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,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(25,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)],[24,23]) ).
tff(26,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),t)),
inference(unit_resolution,[status(thm)],[25,20]) ).
tff(27,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(28,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)],[27]) ).
tff(29,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(30,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(31,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)],[30]) ).
tff(32,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/sandbox/benchmark/theBenchmark.p',fact_256_pos__zmult__pos) ).
tff(33,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)],[32,31]) ).
tff(34,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)],[33,29]) ).
tff(35,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)],[34]) ).
tff(36,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)],[35,28]) ).
tff(37,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(38,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/sandbox/benchmark/theBenchmark.p',fact_6_p0) ).
tff(39,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)],[38,37]) ).
tff(40,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(pls))))),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(pls))))),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(pls))))),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(pls))))),m)),one_one(int))),t))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,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(pls))))),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(pls))))),m)),one_one(int))),t))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,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(pls))))),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(pls))))),m)),one_one(int))),t))) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,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(pls))))),m)),one_one(int))),t))) ),
inference(unit_resolution,[status(thm)],[42,39,36]) ).
tff(44,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(pls))))),m)),one_one(int))),t))),
inference(unit_resolution,[status(thm)],[43,26]) ).
tff(45,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))),
inference(modus_ponens,[status(thm)],[44,11]) ).
tff(46,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(47,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/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
tff(48,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)],[47,46]) ).
tff(49,plain,
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))) = 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)),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
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)) = 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)),pls),
inference(monotonicity,[status(thm)],[49,7]) ).
tff(51,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,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)),pls)) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,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,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)),pls)) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,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(54,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(55,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)],[54,53]) ).
tff(56,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)),pls)),
inference(modus_ponens,[status(thm)],[55,52]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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(61,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)],[60]) ).
tff(62,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/sandbox/benchmark/theBenchmark.p',fact_92_zless__linear) ).
tff(63,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)],[62,61]) ).
tff(64,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)],[63,59]) ).
tff(65,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)],[64]) ).
tff(66,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)],[65,58]) ).
tff(67,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(pls))))),m)),one_one(int))),t)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),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(pls))))),m)),one_one(int))),t)) = ti(int,pls) ) )
<=> ( ~ ! [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(pls))))),m)),one_one(int))),t)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),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(pls))))),m)),one_one(int))),t)) = ti(int,pls) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,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(pls))))),m)),one_one(int))),t)) = ti(int,pls) )
| 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)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),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(pls))))),m)),one_one(int))),t)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),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(pls))))),m)),one_one(int))),t)) = ti(int,pls) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,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,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)) = ti(int,pls) )
| 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)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),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(pls))))),m)),one_one(int))),t)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),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(pls))))),m)),one_one(int))),t)) = ti(int,pls) ) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,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,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)) = ti(int,pls) )
| 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)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),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(pls))))),m)),one_one(int))),t)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),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(pls))))),m)),one_one(int))),t)) = ti(int,pls) ) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,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,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)) = ti(int,pls) )
| 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)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,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(pls))))),m)),one_one(int))),t)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),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(pls))))),m)),one_one(int))),t)) = ti(int,pls) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,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(pls))))),m)),one_one(int))),t)) = ti(int,pls),
inference(unit_resolution,[status(thm)],[72,66,56,45]) ).
tff(74,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(75,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)],[74]) ).
tff(76,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(77,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/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
tff(78,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)],[77,76]) ).
tff(79,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)],[78]) ).
tff(80,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)],[79,75]) ).
tff(81,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(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))),t) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,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(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))),t),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),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(pls))))),m)),one_one(int))),t)),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( semiring_1(int)
<=> semiring_1(int) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
tff(86,plain,
semiring_1(int),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
^ [X_a: $i] :
refl(( ( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) )
<=> ( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [X_a: $i] :
( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) )
<=> ! [X_a: $i] :
( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [X_a: $i] :
( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) )
<=> ! [X_a: $i] :
( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
^ [X_a: $i] :
rewrite(( ( semiring_1(X_a)
=> ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) )
<=> ( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(91,plain,
( ! [X_a: $i] :
( semiring_1(X_a)
=> ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) )
<=> ! [X_a: $i] :
( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,axiom,
! [X_a: $i] :
( semiring_1(X_a)
=> ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_one__power2) ).
tff(93,plain,
! [X_a: $i] :
( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [X_a: $i] :
( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
! [X_a: $i] :
( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [X_a: $i] :
( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) ),
inference(modus_ponens,[status(thm)],[95,88]) ).
tff(97,plain,
( ( ~ ! [X_a: $i] :
( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) )
| ~ semiring_1(int)
| ( hAPP(nat,int,power_power(int,one_one(int)),number_number_of(nat,bit0(bit1(pls)))) = one_one(int) ) )
<=> ( ~ ! [X_a: $i] :
( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) )
| ~ semiring_1(int)
| ( hAPP(nat,int,power_power(int,one_one(int)),number_number_of(nat,bit0(bit1(pls)))) = one_one(int) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [X_a: $i] :
( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) )
| ~ semiring_1(int)
| ( hAPP(nat,int,power_power(int,one_one(int)),number_number_of(nat,bit0(bit1(pls)))) = one_one(int) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [X_a: $i] :
( ~ semiring_1(X_a)
| ( hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a) ) )
| ~ semiring_1(int)
| ( hAPP(nat,int,power_power(int,one_one(int)),number_number_of(nat,bit0(bit1(pls)))) = one_one(int) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
hAPP(nat,int,power_power(int,one_one(int)),number_number_of(nat,bit0(bit1(pls)))) = one_one(int),
inference(unit_resolution,[status(thm)],[99,96,86]) ).
tff(101,plain,
( ( one_one(int) = number_number_of(int,bit1(pls)) )
<=> ( one_one(int) = number_number_of(int,bit1(pls)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_one__is__num__one) ).
tff(103,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
number_number_of(int,bit1(pls)) = one_one(int),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
power_power(int,number_number_of(int,bit1(pls))) = power_power(int,one_one(int)),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
hAPP(nat,int,power_power(int,number_number_of(int,bit1(pls))),number_number_of(nat,bit0(bit1(pls)))) = hAPP(nat,int,power_power(int,one_one(int)),number_number_of(nat,bit0(bit1(pls)))),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
hAPP(nat,int,power_power(int,number_number_of(int,bit1(pls))),number_number_of(nat,bit0(bit1(pls)))) = one_one(int),
inference(transitivity,[status(thm)],[106,100]) ).
tff(108,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,number_number_of(int,bit1(pls))),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,number_number_of(int,bit1(pls))),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(int),
inference(transitivity,[status(thm)],[108,48,83,73,6,3]) ).
tff(110,plain,
( linordered_idom(int)
<=> linordered_idom(int) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,axiom,
linordered_idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(112,plain,
linordered_idom(int),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
^ [X_a: $i] :
refl(( ( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) )
<=> ( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
^ [X_a: $i] :
rewrite(( ( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) )
<=> ( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(116,plain,
( ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) ) ),
inference(transitivity,[status(thm)],[116,114]) ).
tff(118,plain,
^ [X_a: $i] :
rewrite(( ( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
( ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) )
<=> ( ( ti(X_a,X) = zero_zero(X_a) )
& ( ti(X_a,Y_1) = zero_zero(X_a) ) ) ) )
<=> ( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
( ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) )
<=> ( ( ti(X_a,X) = zero_zero(X_a) )
& ( ti(X_a,Y_1) = zero_zero(X_a) ) ) ) )
<=> ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
( ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) )
<=> ( ( ti(X_a,X) = zero_zero(X_a) )
& ( ti(X_a,Y_1) = zero_zero(X_a) ) ) ) )
<=> ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
( ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) )
<=> ( ( ti(X_a,X) = zero_zero(X_a) )
& ( ti(X_a,Y_1) = zero_zero(X_a) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
^ [X_a: $i] :
rewrite(( ( linordered_idom(X_a)
=> ! [X: $i,Y_1: $i] :
( ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) )
<=> ( ( ti(X_a,X) = zero_zero(X_a) )
& ( ti(X_a,Y_1) = zero_zero(X_a) ) ) ) )
<=> ( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
( ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) )
<=> ( ( ti(X_a,X) = zero_zero(X_a) )
& ( ti(X_a,Y_1) = zero_zero(X_a) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(122,plain,
( ! [X_a: $i] :
( linordered_idom(X_a)
=> ! [X: $i,Y_1: $i] :
( ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) )
<=> ( ( ti(X_a,X) = zero_zero(X_a) )
& ( ti(X_a,Y_1) = zero_zero(X_a) ) ) ) )
<=> ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
( ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) )
<=> ( ( ti(X_a,X) = zero_zero(X_a) )
& ( ti(X_a,Y_1) = zero_zero(X_a) ) ) ) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,axiom,
! [X_a: $i] :
( linordered_idom(X_a)
=> ! [X: $i,Y_1: $i] :
( ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) )
<=> ( ( ti(X_a,X) = zero_zero(X_a) )
& ( ti(X_a,Y_1) = zero_zero(X_a) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_sum__power2__eq__zero__iff) ).
tff(124,plain,
! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
( ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) )
<=> ( ( ti(X_a,X) = zero_zero(X_a) )
& ( ti(X_a,Y_1) = zero_zero(X_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
( ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) )
<=> ( ( ti(X_a,X) = zero_zero(X_a) )
& ( ti(X_a,Y_1) = zero_zero(X_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[124,120]) ).
tff(126,plain,
! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
( ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) )
<=> ( ( ti(X_a,X) = zero_zero(X_a) )
& ( ti(X_a,Y_1) = zero_zero(X_a) ) ) ) ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,plain,
! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) ),
inference(modus_ponens,[status(thm)],[126,119]) ).
tff(128,plain,
! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) ),
inference(modus_ponens,[status(thm)],[127,117]) ).
tff(129,plain,
( ( ~ ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) )
| ~ linordered_idom(int)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(int,Y_1) != zero_zero(int) )
| ( ti(int,X) != zero_zero(int) ) )
<=> ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(int) ) ) )
<=> ( ~ ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) )
| ~ linordered_idom(int)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(int,Y_1) != zero_zero(int) )
| ( ti(int,X) != zero_zero(int) ) )
<=> ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(int) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
( ~ ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) )
| ~ linordered_idom(int)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(int,Y_1) != zero_zero(int) )
| ( ti(int,X) != zero_zero(int) ) )
<=> ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(int) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [X_a: $i] :
( ~ linordered_idom(X_a)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(X_a,Y_1) != zero_zero(X_a) )
| ( ti(X_a,X) != zero_zero(X_a) ) )
<=> ( hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,X_a,power_power(X_a,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a) ) ) )
| ~ linordered_idom(int)
| ! [X: $i,Y_1: $i] :
~ ( ( ( ti(int,Y_1) != zero_zero(int) )
| ( ti(int,X) != zero_zero(int) ) )
<=> ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(int) ) ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [X: $i,Y_1: $i] :
~ ( ( ( ti(int,Y_1) != zero_zero(int) )
| ( ti(int,X) != zero_zero(int) ) )
<=> ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(int) ) ),
inference(unit_resolution,[status(thm)],[131,128,112]) ).
tff(133,plain,
( ~ ! [X: $i,Y_1: $i] :
~ ( ( ( ti(int,Y_1) != zero_zero(int) )
| ( ti(int,X) != zero_zero(int) ) )
<=> ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y_1),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(int) ) )
| ~ ( ( ( ti(int,number_number_of(int,bit1(pls))) != zero_zero(int) )
| ( ti(int,s) != zero_zero(int) ) )
<=> ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,number_number_of(int,bit1(pls))),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(int) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
~ ( ( ( ti(int,number_number_of(int,bit1(pls))) != zero_zero(int) )
| ( ti(int,s) != zero_zero(int) ) )
<=> ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,number_number_of(int,bit1(pls))),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(int) ) ),
inference(unit_resolution,[status(thm)],[133,132]) ).
tff(135,plain,
( ( ti(int,number_number_of(int,bit1(pls))) = ti(int,pls) )
<=> ( ti(int,pls) = ti(int,number_number_of(int,bit1(pls))) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(136,plain,
pls = ti(int,pls),
inference(symmetry,[status(thm)],[6]) ).
tff(137,plain,
zero_zero(int) = ti(int,pls),
inference(transitivity,[status(thm)],[7,136]) ).
tff(138,plain,
( ( ti(int,number_number_of(int,bit1(pls))) = zero_zero(int) )
<=> ( ti(int,number_number_of(int,bit1(pls))) = ti(int,pls) ) ),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
( ( ti(int,number_number_of(int,bit1(pls))) = zero_zero(int) )
<=> ( ti(int,pls) = ti(int,number_number_of(int,bit1(pls))) ) ),
inference(transitivity,[status(thm)],[138,135]) ).
tff(140,plain,
( ( ti(int,pls) = ti(int,number_number_of(int,bit1(pls))) )
<=> ( ti(int,number_number_of(int,bit1(pls))) = zero_zero(int) ) ),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
( number(int)
<=> number(int) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,axiom,
number(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
tff(143,plain,
number(int),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,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(145,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)],[144]) ).
tff(146,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(147,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(148,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)],[147]) ).
tff(149,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/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
tff(150,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)],[149,148]) ).
tff(151,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)],[150,146]) ).
tff(152,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)],[151]) ).
tff(153,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)],[152,145]) ).
tff(154,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(pls))) = number_number_of(int,bit1(pls)) ) )
<=> ( ~ ! [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(pls))) = number_number_of(int,bit1(pls)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,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(pls))) = number_number_of(int,bit1(pls)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,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(pls))) = number_number_of(int,bit1(pls)) ) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
ti(int,number_number_of(int,bit1(pls))) = number_number_of(int,bit1(pls)),
inference(unit_resolution,[status(thm)],[156,153,143]) ).
tff(158,plain,
ti(int,number_number_of(int,bit1(pls))) = one_one(int),
inference(transitivity,[status(thm)],[157,104]) ).
tff(159,plain,
ti(int,pls) = zero_zero(int),
inference(transitivity,[status(thm)],[6,3]) ).
tff(160,plain,
( ( ti(int,pls) = ti(int,number_number_of(int,bit1(pls))) )
<=> ( zero_zero(int) = one_one(int) ) ),
inference(monotonicity,[status(thm)],[159,158]) ).
tff(161,plain,
( ( zero_zero(int) = one_one(int) )
<=> ( ti(int,pls) = ti(int,number_number_of(int,bit1(pls))) ) ),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
( ( zero_zero(int) = one_one(int) )
<=> ( ti(int,number_number_of(int,bit1(pls))) = zero_zero(int) ) ),
inference(transitivity,[status(thm)],[161,140]) ).
tff(163,plain,
( ( zero_zero(int) != one_one(int) )
<=> ( ti(int,number_number_of(int,bit1(pls))) != zero_zero(int) ) ),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ( zero_zero(int) != one_one(int) )
<=> ( zero_zero(int) != one_one(int) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,axiom,
zero_zero(int) != one_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_int__0__neq__1) ).
tff(166,plain,
zero_zero(int) != one_one(int),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
ti(int,number_number_of(int,bit1(pls))) != zero_zero(int),
inference(modus_ponens,[status(thm)],[166,163]) ).
tff(168,plain,
( ( ti(int,number_number_of(int,bit1(pls))) != zero_zero(int) )
| ( ti(int,s) != zero_zero(int) )
| ( ti(int,number_number_of(int,bit1(pls))) = zero_zero(int) ) ),
inference(tautology,[status(thm)],[]) ).
tff(169,plain,
( ( ti(int,number_number_of(int,bit1(pls))) != zero_zero(int) )
| ( ti(int,s) != zero_zero(int) ) ),
inference(unit_resolution,[status(thm)],[168,167]) ).
tff(170,plain,
( ( ( ( ti(int,number_number_of(int,bit1(pls))) != zero_zero(int) )
| ( ti(int,s) != zero_zero(int) ) )
<=> ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,number_number_of(int,bit1(pls))),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(int) ) )
| ~ ( ( ti(int,number_number_of(int,bit1(pls))) != zero_zero(int) )
| ( ti(int,s) != zero_zero(int) ) )
| ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,number_number_of(int,bit1(pls))),number_number_of(nat,bit0(bit1(pls))))) != zero_zero(int) ) ),
inference(tautology,[status(thm)],[]) ).
tff(171,plain,
( ( ( ( ti(int,number_number_of(int,bit1(pls))) != zero_zero(int) )
| ( ti(int,s) != zero_zero(int) ) )
<=> ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,number_number_of(int,bit1(pls))),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(int) ) )
| ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,number_number_of(int,bit1(pls))),number_number_of(nat,bit0(bit1(pls))))) != zero_zero(int) ) ),
inference(unit_resolution,[status(thm)],[170,169]) ).
tff(172,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,number_number_of(int,bit1(pls))),number_number_of(nat,bit0(bit1(pls))))) != zero_zero(int),
inference(unit_resolution,[status(thm)],[171,134]) ).
tff(173,plain,
$false,
inference(unit_resolution,[status(thm)],[172,109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM924+7 : TPTP v9.0.0. Released v5.3.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.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 Jun 20 02:04:33 EDT 2025
% 0.13/0.34 % CPUTime :
% 248.21/248.54 % SZS status Theorem
% 248.21/248.54 % SZS output start Proof
% See solution above
% 248.96/249.25 % E exiting
%------------------------------------------------------------------------------