TSTP Solution File: NUM924+5 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM924+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 13:12:40 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 34
% Syntax : Number of formulae : 63 ( 32 unt; 15 typ; 0 def)
% Number of atoms : 70 ( 48 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 10 ~; 3 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 9 >; 9 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 40 ( 36 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(ord_less_type,type,
ord_less: ( $i * $i * $i ) > $o ).
tff(times_times_type,type,
times_times: ( $i * $i * $i ) > $i ).
tff(zero_zero_type,type,
zero_zero: $i > $i ).
tff(int_type,type,
int: $i ).
tff(plus_plus_type,type,
plus_plus: ( $i * $i * $i ) > $i ).
tff(one_one_type,type,
one_one: $i > $i ).
tff(m_type,type,
m: $i ).
tff(number_number_of_type,type,
number_number_of: ( $i * $i ) > $i ).
tff(bit0_type,type,
bit0: $i > $i ).
tff(bit1_type,type,
bit1: $i > $i ).
tff(pls_type,type,
pls: $i ).
tff(power_power_type,type,
power_power: ( $i * $i * $i ) > $i ).
tff(nat_type,type,
nat: $i ).
tff(s_type,type,
s: $i ).
tff(t_type,type,
t: $i ).
tff(1,plain,
( ( zero_zero(int) = number_number_of(int,pls) )
<=> ( zero_zero(int) = number_number_of(int,pls) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_zero__is__num__zero) ).
tff(3,plain,
zero_zero(int) = number_number_of(int,pls),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
number_number_of(int,pls) = zero_zero(int),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
^ [K_1: $i] :
refl(
( ( number_number_of(int,K_1) = K_1 )
<=> ( number_number_of(int,K_1) = K_1 ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [K_1: $i] : ( number_number_of(int,K_1) = K_1 )
<=> ! [K_1: $i] : ( number_number_of(int,K_1) = K_1 ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [K_1: $i] : ( number_number_of(int,K_1) = K_1 )
<=> ! [K_1: $i] : ( number_number_of(int,K_1) = K_1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
! [K_1: $i] : ( number_number_of(int,K_1) = K_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
tff(9,plain,
! [K_1: $i] : ( number_number_of(int,K_1) = K_1 ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
! [K_1: $i] : ( number_number_of(int,K_1) = K_1 ),
inference(skolemize,[status(sab)],[9]) ).
tff(11,plain,
! [K_1: $i] : ( number_number_of(int,K_1) = K_1 ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
( ~ ! [K_1: $i] : ( number_number_of(int,K_1) = K_1 )
| ( number_number_of(int,pls) = pls ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
number_number_of(int,pls) = pls,
inference(unit_resolution,[status(thm)],[12,11]) ).
tff(14,plain,
pls = number_number_of(int,pls),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
^ [W: $i] :
refl(
( ( times_times(int,pls,W) = pls )
<=> ( times_times(int,pls,W) = pls ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [W: $i] : ( times_times(int,pls,W) = pls )
<=> ! [W: $i] : ( times_times(int,pls,W) = pls ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [W: $i] : ( times_times(int,pls,W) = pls )
<=> ! [W: $i] : ( times_times(int,pls,W) = pls ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [W: $i] : ( times_times(int,pls,W) = pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
tff(19,plain,
! [W: $i] : ( times_times(int,pls,W) = pls ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [W: $i] : ( times_times(int,pls,W) = pls ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [W: $i] : ( times_times(int,pls,W) = pls ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [W: $i] : ( times_times(int,pls,W) = pls )
| ( times_times(int,pls,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) = pls ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
times_times(int,pls,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) = pls,
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
times_times(int,number_number_of(int,pls),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) = times_times(int,pls,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(monotonicity,[status(thm)],[13]) ).
tff(25,plain,
^ [Z: $i,W: $i] :
refl(
( ( times_times(int,Z,W) = times_times(int,W,Z) )
<=> ( times_times(int,Z,W) = times_times(int,W,Z) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) )
<=> ! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) )
<=> ! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
tff(29,plain,
! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) )
| ( times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,pls)) = times_times(int,number_number_of(int,pls),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,pls)) = times_times(int,number_number_of(int,pls),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,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)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,pls)),
inference(monotonicity,[status(thm)],[3]) ).
tff(35,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(transitivity,[status(thm)],[34,33,24,23,14,4]) ).
tff(36,plain,
( ord_less(int,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)),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)],[35]) ).
tff(37,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)),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)],[36]) ).
tff(38,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)),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)],[37]) ).
tff(39,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(40,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(41,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)],[40,39]) ).
tff(42,plain,
~ ord_less(int,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)),zero_zero(int))),
inference(modus_ponens,[status(thm)],[41,38]) ).
tff(43,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)),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(44,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(45,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/sandbox/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(46,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)],[45,44]) ).
tff(47,plain,
ord_less(int,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)),zero_zero(int))),
inference(modus_ponens,[status(thm)],[46,43]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM924+5 : TPTP v8.1.0. Released v5.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 16:08:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------