TSTP Solution File: NUM924_2 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM924_2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:12:38 EDT 2022
% Result : Theorem 0.17s 0.57s
% Output : Proof 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of formulae : 50 ( 20 unt; 16 typ; 0 def)
% Number of atoms : 54 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 14 ~; 1 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 9 >; 5 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 18 ( 15 !; 0 ?; 18 :)
% 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(pls_type,type,
pls: int ).
tff(plus_plus_int_type,type,
plus_plus_int: ( int * int ) > int ).
tff(number_number_of_int_type,type,
number_number_of_int: int > int ).
tff(bit1_type,type,
bit1: int > int ).
tff(m_type,type,
m: int ).
tff(bit0_type,type,
bit0: int > int ).
tff(minus_minus_int_type,type,
minus_minus_int: ( int * int ) > int ).
tff(min_type,type,
min: 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(zero_zero_int_type,type,
zero_zero_int: int ).
tff(one_one_int_type,type,
one_one_int: int ).
tff(t_type,type,
t: int ).
tff(1,plain,
^ [A_37: int] :
refl(
( ( times_times_int(A_37,pls) = pls )
<=> ( times_times_int(A_37,pls) = pls ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A_37: int] : ( times_times_int(A_37,pls) = pls )
<=> ! [A_37: int] : ( times_times_int(A_37,pls) = pls ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [A_37: int] :
rewrite(
( ( times_times_int(A_37,number_number_of_int(pls)) = number_number_of_int(pls) )
<=> ( times_times_int(A_37,pls) = pls ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [A_37: int] : ( times_times_int(A_37,number_number_of_int(pls)) = number_number_of_int(pls) )
<=> ! [A_37: int] : ( times_times_int(A_37,pls) = pls ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [A_37: int] :
rewrite(
( ( times_times_int(A_37,zero_zero_int) = zero_zero_int )
<=> ( times_times_int(A_37,number_number_of_int(pls)) = number_number_of_int(pls) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [A_37: int] : ( times_times_int(A_37,zero_zero_int) = zero_zero_int )
<=> ! [A_37: int] : ( times_times_int(A_37,number_number_of_int(pls)) = number_number_of_int(pls) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,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(8,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(9,plain,
! [A_37: int] : ( times_times_int(A_37,zero_zero_int) = zero_zero_int ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
! [A_37: int] : ( times_times_int(A_37,number_number_of_int(pls)) = number_number_of_int(pls) ),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
! [A_37: int] : ( times_times_int(A_37,pls) = pls ),
inference(modus_ponens,[status(thm)],[10,4]) ).
tff(12,plain,
! [A_37: int] : ( times_times_int(A_37,pls) = pls ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [A_37: int] : ( times_times_int(A_37,pls) = pls ),
inference(modus_ponens,[status(thm)],[12,2]) ).
tff(14,plain,
( ~ ! [A_37: int] : ( times_times_int(A_37,pls) = pls )
| ( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),number_number_of_int(bit1(pls))),pls) = pls ) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),number_number_of_int(bit1(pls))),pls) = pls,
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
( ord_less_int(minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),number_number_of_int(bit1(pls))),pls))
<=> ord_less_int(minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),pls) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ord_less_int(minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),pls)
<=> ord_less_int(minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),number_number_of_int(bit1(pls))),pls)) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( ~ ord_less_int(minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),pls)
<=> ~ ord_less_int(minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),number_number_of_int(bit1(pls))),pls)) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(bit1(pls))),number_number_of_int(pls))
<=> ~ ord_less_int(minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),pls) ),
inference(rewrite,[status(thm)],]) ).
tff(20,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)))),number_number_of_int(bit1(pls))),number_number_of_int(pls)) ),
inference(rewrite,[status(thm)],]) ).
tff(21,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(22,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(23,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)],[22,21]) ).
tff(24,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(bit1(pls))),number_number_of_int(pls)),
inference(modus_ponens,[status(thm)],[23,20]) ).
tff(25,plain,
~ ord_less_int(minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),pls),
inference(modus_ponens,[status(thm)],[24,19]) ).
tff(26,plain,
~ ord_less_int(minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),number_number_of_int(bit1(pls))),pls)),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
( ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),number_number_of_int(bit1(pls))),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),number_number_of_int(bit1(pls))),number_number_of_int(pls)))
<=> ord_less_int(minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),number_number_of_int(bit1(pls))),pls)) ),
inference(rewrite,[status(thm)],]) ).
tff(28,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),number_number_of_int(bit1(pls))),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),number_number_of_int(bit1(pls))),number_number_of_int(pls))) ),
inference(rewrite,[status(thm)],]) ).
tff(29,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(30,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(31,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)],[30,29]) ).
tff(32,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),number_number_of_int(bit1(pls))),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),number_number_of_int(bit1(pls))),number_number_of_int(pls))),
inference(modus_ponens,[status(thm)],[31,28]) ).
tff(33,plain,
ord_less_int(minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),number_number_of_int(bit1(pls))),pls)),
inference(modus_ponens,[status(thm)],[32,27]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM924_2 : TPTP v8.1.0. Released v5.3.0.
% 0.00/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n025.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Sep 2 15:52:47 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.17/0.57 % SZS status Theorem
% 0.17/0.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------