%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM924_2 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:22:21 AM UTC 2025
% Result : Theorem 0.40s 0.59s
% Output : Proof 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 24 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 8 ~; 1 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 10 ( 9 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(ord_less_int_type,type,
ord_less_int: ( int * int ) > $o ).
tff(times_times_int_type,type,
times_times_int: ( int * int ) > int ).
tff(zero_zero_int_type,type,
zero_zero_int: int ).
tff(plus_plus_int_type,type,
plus_plus_int: ( int * int ) > int ).
tff(one_one_int_type,type,
one_one_int: int ).
tff(m_type,type,
m: int ).
tff(number_number_of_int_type,type,
number_number_of_int: int > int ).
tff(bit0_type,type,
bit0: int > int ).
tff(bit1_type,type,
bit1: int > int ).
tff(pls_type,type,
pls: int ).
tff(t_type,type,
t: int ).
tff(power_power_int_type,type,
power_power_int: ( int * nat ) > int ).
tff(number_number_of_nat_type,type,
number_number_of_nat: int > nat ).
tff(s_type,type,
s: int ).
tff(1,plain,
^ [A_37: int] :
refl(( ( times_times_int(A_37,zero_zero_int) = zero_zero_int )
<=> ( times_times_int(A_37,zero_zero_int) = zero_zero_int ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A_37: int] : ( times_times_int(A_37,zero_zero_int) = zero_zero_int )
<=> ! [A_37: int] : ( times_times_int(A_37,zero_zero_int) = zero_zero_int ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A_37: int] : ( times_times_int(A_37,zero_zero_int) = zero_zero_int )
<=> ! [A_37: int] : ( times_times_int(A_37,zero_zero_int) = zero_zero_int ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [A_37: int] : ( times_times_int(A_37,zero_zero_int) = zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
tff(5,plain,
! [A_37: int] : ( times_times_int(A_37,zero_zero_int) = zero_zero_int ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A_37: int] : ( times_times_int(A_37,zero_zero_int) = zero_zero_int ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A_37: int] : ( times_times_int(A_37,zero_zero_int) = zero_zero_int ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A_37: int] : ( times_times_int(A_37,zero_zero_int) = zero_zero_int )
| ( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int) = zero_zero_int ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int) = zero_zero_int,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) )
<=> ( plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_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(12,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int))
<=> ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int) ),
inference(monotonicity,[status(thm)],[13,9]) ).
tff(15,plain,
( ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int)
<=> ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)) ),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int)
<=> ~ ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int)
<=> ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
~ ord_less_int(plus_plus_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(19,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
( ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int))
<=> ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_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(23,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
$false,
inference(unit_resolution,[status(thm)],[23,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : NUM924_2 : TPTP v9.0.0. Released v5.3.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 02:03:40 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.40/0.59 % SZS status Theorem
% 0.40/0.59 % SZS output start Proof
% See solution above
% 0.49/0.63 % E exiting
%------------------------------------------------------------------------------