%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM924_3 : 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 05:22:22 AM UTC 2025
% Result : Theorem 0.70s 0.89s
% Output : Proof 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 32 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 115 ( 6 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 128 ( 53 ~; 49 |; 0 &)
% ( 15 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 8 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-2 aty)
% Number of variables : 34 ( 30 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: bool > $o ).
tff(hAPP_int_bool_type,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(zero_zero_int_type,type,
zero_zero_int: int ).
tff(hAPP_i1948725293t_bool_type,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(hAPP_int_int_type,type,
hAPP_int_int: ( fun_int_int * int ) > int ).
tff(one_one_int_type,type,
one_one_int: int ).
tff(plus_plus_int_type,type,
plus_plus_int: int > fun_int_int ).
tff(hAPP_nat_int_type,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(number_number_of_nat_type,type,
number_number_of_nat: int > nat ).
tff(bit0_type,type,
bit0: int > int ).
tff(bit1_type,type,
bit1: int > int ).
tff(pls_type,type,
pls: int ).
tff(power_power_int_type,type,
power_power_int: int > fun_nat_int ).
tff(s_type,type,
s: int ).
tff(ord_less_int_type,type,
ord_less_int: fun_int_fun_int_bool ).
tff(t_type,type,
t: int ).
tff(times_times_int_type,type,
times_times_int: int > fun_int_int ).
tff(m_type,type,
m: int ).
tff(number_number_of_int_type,type,
number_number_of_int: int > int ).
tff(1,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(2,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(3,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)],[2,1]) ).
tff(4,plain,
hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)) = hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),zero_zero_int),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(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)),zero_zero_int)) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
^ [B_17: int,A_25: int] :
refl(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) )
<=> ! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) )
<=> ! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
^ [B_17: int,A_25: int] :
trans(monotonicity(rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int)) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int)) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int)) ) ) )),
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int)) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int)) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int)) ) )
<=> ! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,axiom,
! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_mult__pos__neg) ).
tff(14,plain,
! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_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_i1948725293t_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(19,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_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(20,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_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)],[19,18]) ).
tff(21,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),zero_zero_int)) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096t_A_060_A0_096) ).
tff(23,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,t),zero_zero_int)),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ( ~ ! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_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_i1948725293t_bool(ord_less_int,t),zero_zero_int)) )
<=> ( ~ ! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_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_i1948725293t_bool(ord_less_int,t),zero_zero_int)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_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_i1948725293t_bool(ord_less_int,t),zero_zero_int)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [B_17: int,A_25: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_25),B_17)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_25))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),zero_zero_int)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_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_i1948725293t_bool(ord_less_int,t),zero_zero_int)) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),zero_zero_int)),
inference(unit_resolution,[status(thm)],[26,23,20,17]) ).
tff(28,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
inference(modus_ponens,[status(thm)],[27,7]) ).
tff(29,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(31,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM924_3 : TPTP v9.0.0. Released v5.3.0.
% 0.07/0.13 % 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 02:04:18 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.70/0.89 % SZS status Theorem
% 0.70/0.89 % SZS output start Proof
% See solution above
% 0.78/0.96 % E exiting
%------------------------------------------------------------------------------