TSTP Solution File: NUM926+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM926+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 13:12:45 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 32
% Syntax : Number of formulae : 58 ( 12 unt; 13 typ; 0 def)
% Number of atoms : 136 ( 63 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 161 ( 72 ~; 40 |; 7 &)
% ( 38 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 9 >; 5 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 24 !; 34 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
tff(one_one_int_type,type,
one_one_int: $i ).
tff(t_type,type,
t: $i ).
tff(ord_less_eq_int_type,type,
ord_less_eq_int: ( $i * $i ) > $o ).
tff(ord_less_int_type,type,
ord_less_int: ( $i * $i ) > $o ).
tff(plus_plus_int_type,type,
plus_plus_int: ( $i * $i ) > $i ).
tff(times_times_int_type,type,
times_times_int: ( $i * $i ) > $i ).
tff(m_type,type,
m: $i ).
tff(number_number_of_int_type,type,
number_number_of_int: $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_int_type,type,
power_power_int: ( $i * $i ) > $i ).
tff(number_number_of_nat_type,type,
number_number_of_nat: $i > $i ).
tff(1,plain,
^ [Z_1: $i,W_1: $i] :
refl(
( ( ord_less_int(Z_1,W_1)
<=> ~ ( ~ ord_less_eq_int(Z_1,W_1)
| ( Z_1 = W_1 ) ) )
<=> ( ord_less_int(Z_1,W_1)
<=> ~ ( ~ ord_less_eq_int(Z_1,W_1)
| ( Z_1 = W_1 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z_1: $i,W_1: $i] :
( ord_less_int(Z_1,W_1)
<=> ~ ( ~ ord_less_eq_int(Z_1,W_1)
| ( Z_1 = W_1 ) ) )
<=> ! [Z_1: $i,W_1: $i] :
( ord_less_int(Z_1,W_1)
<=> ~ ( ~ ord_less_eq_int(Z_1,W_1)
| ( Z_1 = W_1 ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [Z_1: $i,W_1: $i] :
rewrite(
( ( ord_less_int(Z_1,W_1)
<=> ( ord_less_eq_int(Z_1,W_1)
& ( Z_1 != W_1 ) ) )
<=> ( ord_less_int(Z_1,W_1)
<=> ~ ( ~ ord_less_eq_int(Z_1,W_1)
| ( Z_1 = W_1 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [Z_1: $i,W_1: $i] :
( ord_less_int(Z_1,W_1)
<=> ( ord_less_eq_int(Z_1,W_1)
& ( Z_1 != W_1 ) ) )
<=> ! [Z_1: $i,W_1: $i] :
( ord_less_int(Z_1,W_1)
<=> ~ ( ~ ord_less_eq_int(Z_1,W_1)
| ( Z_1 = W_1 ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [Z_1: $i,W_1: $i] :
( ord_less_int(Z_1,W_1)
<=> ( ord_less_eq_int(Z_1,W_1)
& ( Z_1 != W_1 ) ) )
<=> ! [Z_1: $i,W_1: $i] :
( ord_less_int(Z_1,W_1)
<=> ( ord_less_eq_int(Z_1,W_1)
& ( Z_1 != W_1 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [Z_1: $i,W_1: $i] :
( ord_less_int(Z_1,W_1)
<=> ( ord_less_eq_int(Z_1,W_1)
& ( Z_1 != W_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_zless__le) ).
tff(7,plain,
! [Z_1: $i,W_1: $i] :
( ord_less_int(Z_1,W_1)
<=> ( ord_less_eq_int(Z_1,W_1)
& ( Z_1 != W_1 ) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [Z_1: $i,W_1: $i] :
( ord_less_int(Z_1,W_1)
<=> ( ord_less_eq_int(Z_1,W_1)
& ( Z_1 != W_1 ) ) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [Z_1: $i,W_1: $i] :
( ord_less_int(Z_1,W_1)
<=> ~ ( ~ ord_less_eq_int(Z_1,W_1)
| ( Z_1 = W_1 ) ) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [Z_1: $i,W_1: $i] :
( ord_less_int(Z_1,W_1)
<=> ~ ( ~ ord_less_eq_int(Z_1,W_1)
| ( Z_1 = W_1 ) ) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [Z_1: $i,W_1: $i] :
( ord_less_int(Z_1,W_1)
<=> ~ ( ~ ord_less_eq_int(Z_1,W_1)
| ( Z_1 = W_1 ) ) )
| ( ord_less_int(one_one_int,t)
<=> ~ ( ~ ord_less_eq_int(one_one_int,t)
| ( one_one_int = t ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
( ord_less_int(one_one_int,t)
<=> ~ ( ~ ord_less_eq_int(one_one_int,t)
| ( one_one_int = t ) ) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( ~ ord_less_int(one_one_int,t)
<=> ~ ord_less_int(one_one_int,t) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ( ~ ord_less_int(one_one_int,t)
| $false )
<=> ~ ord_less_int(one_one_int,t) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
~ ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(16,plain,
( ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) )
<=> $false ),
inference(iff_false,[status(thm)],[15]) ).
tff(17,plain,
( ( ~ ord_less_int(one_one_int,t)
| ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) )
<=> ( ~ ord_less_int(one_one_int,t)
| $false ) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ( ~ ord_less_int(one_one_int,t)
| ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) )
<=> ~ ord_less_int(one_one_int,t) ),
inference(transitivity,[status(thm)],[17,14]) ).
tff(19,plain,
( ( ord_less_int(one_one_int,t)
=> ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) )
<=> ( ~ ord_less_int(one_one_int,t)
| ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
( ord_less_int(one_one_int,t)
=> ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
tff(21,plain,
( ~ ord_less_int(one_one_int,t)
| ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
~ ord_less_int(one_one_int,t),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
~ ord_less_int(one_one_int,t),
inference(modus_ponens,[status(thm)],[22,13]) ).
tff(24,plain,
( ~ ( ord_less_int(one_one_int,t)
<=> ~ ( ~ ord_less_eq_int(one_one_int,t)
| ( one_one_int = t ) ) )
| ord_less_int(one_one_int,t)
| ~ ord_less_eq_int(one_one_int,t)
| ( one_one_int = t ) ),
inference(tautology,[status(thm)],]) ).
tff(25,plain,
( ~ ( ord_less_int(one_one_int,t)
<=> ~ ( ~ ord_less_eq_int(one_one_int,t)
| ( one_one_int = t ) ) )
| ~ ord_less_eq_int(one_one_int,t)
| ( one_one_int = t ) ),
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
( ~ ord_less_eq_int(one_one_int,t)
| ( one_one_int = t ) ),
inference(unit_resolution,[status(thm)],[25,12]) ).
tff(27,plain,
( ord_less_eq_int(one_one_int,t)
<=> ord_less_eq_int(one_one_int,t) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
ord_less_eq_int(one_one_int,t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
tff(29,plain,
ord_less_eq_int(one_one_int,t),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ( ~ ord_less_eq_int(one_one_int,t)
| ( one_one_int = t ) )
| ~ ord_less_eq_int(one_one_int,t)
| ( one_one_int = t ) ),
inference(tautology,[status(thm)],]) ).
tff(31,plain,
( ~ ( ~ ord_less_eq_int(one_one_int,t)
| ( one_one_int = t ) )
| ( one_one_int = t ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
one_one_int = t,
inference(unit_resolution,[status(thm)],[31,26]) ).
tff(33,plain,
t = one_one_int,
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ( t != one_one_int )
<=> ( t != one_one_int ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( ( t != one_one_int )
| $false )
<=> ( t != one_one_int ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ( t != one_one_int )
| ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) )
<=> ( ( t != one_one_int )
| $false ) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(37,plain,
( ( ( t != one_one_int )
| ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) )
<=> ( t != one_one_int ) ),
inference(transitivity,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ( t != one_one_int )
| ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) )
<=> ( ( t != one_one_int )
| ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ( ( t = one_one_int )
=> ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) )
<=> ( ( t != one_one_int )
| ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
( ( t = one_one_int )
=> ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
tff(41,plain,
( ( t != one_one_int )
| ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( t != one_one_int )
| ? [X: $i,Y: $i] : ( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ),
inference(modus_ponens,[status(thm)],[41,38]) ).
tff(43,plain,
t != one_one_int,
inference(modus_ponens,[status(thm)],[42,37]) ).
tff(44,plain,
t != one_one_int,
inference(modus_ponens,[status(thm)],[43,34]) ).
tff(45,plain,
$false,
inference(unit_resolution,[status(thm)],[44,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : NUM926+1 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n002.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 Sep 2 16:01:46 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------