TSTP Solution File: NUM925_2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM925_2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n032.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 : Thu Aug 31 12:16:48 EDT 2023
% Result : Theorem 0.25s 0.51s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 91
% Syntax : Number of formulae : 108 ( 12 unt; 86 typ; 0 def)
% Number of atoms : 42 ( 14 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 38 ( 18 ~; 10 |; 6 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 16 ( 15 usr)
% Number of type conns : 72 ( 49 >; 23 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 70 ( 70 usr; 22 con; 0-2 aty)
% Number of variables : 19 (; 19 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
real: $tType ).
tff(type_def_9,type,
fun_int_bool: $tType ).
tff(type_def_10,type,
fun_int_int: $tType ).
tff(type_def_11,type,
fun_int_fun_int_bool: $tType ).
tff(type_def_12,type,
fun_nat_bool: $tType ).
tff(type_def_13,type,
fun_nat_int: $tType ).
tff(type_def_14,type,
fun_nat_nat: $tType ).
tff(type_def_15,type,
fun_nat_real: $tType ).
tff(type_def_16,type,
fun_nat_fun_nat_bool: $tType ).
tff(type_def_17,type,
fun_real_bool: $tType ).
tff(type_def_18,type,
fun_real_real: $tType ).
tff(type_def_19,type,
fun_re413263731l_bool: $tType ).
tff(func_def_0,type,
one_one_int: int ).
tff(func_def_1,type,
one_one_nat: nat ).
tff(func_def_2,type,
one_one_real: real ).
tff(func_def_3,type,
plus_plus_int: int > fun_int_int ).
tff(func_def_4,type,
plus_plus_nat: nat > fun_nat_nat ).
tff(func_def_5,type,
plus_plus_real: real > fun_real_real ).
tff(func_def_6,type,
times_times_int: ( int * int ) > int ).
tff(func_def_7,type,
zero_zero_int: int ).
tff(func_def_8,type,
zero_zero_nat: nat ).
tff(func_def_9,type,
zero_zero_real: real ).
tff(func_def_10,type,
if_nat: ( bool * nat ) > fun_nat_nat ).
tff(func_def_11,type,
bit0: int > int ).
tff(func_def_12,type,
bit1: int > int ).
tff(func_def_13,type,
pls: int ).
tff(func_def_14,type,
number_number_of_int: int > int ).
tff(func_def_15,type,
number_number_of_nat: int > nat ).
tff(func_def_16,type,
number267125858f_real: int > real ).
tff(func_def_17,type,
succ: int > int ).
tff(func_def_18,type,
semiri1621563631at_int: fun_nat_int ).
tff(func_def_19,type,
semiri984289939at_nat: fun_nat_nat ).
tff(func_def_20,type,
semiri132038758t_real: fun_nat_real ).
tff(func_def_21,type,
sqrt: real > real ).
tff(func_def_22,type,
ord_less_int: fun_int_fun_int_bool ).
tff(func_def_23,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(func_def_24,type,
ord_less_real: fun_re413263731l_bool ).
tff(func_def_25,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(func_def_26,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(func_def_27,type,
ord_less_eq_real: fun_re413263731l_bool ).
tff(func_def_28,type,
power_power_int: int > fun_nat_int ).
tff(func_def_29,type,
power_power_nat: nat > fun_nat_nat ).
tff(func_def_30,type,
power_power_real: real > fun_nat_real ).
tff(func_def_31,type,
fFalse: bool ).
tff(func_def_32,type,
fTrue: bool ).
tff(func_def_33,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(func_def_34,type,
hAPP_int_int: ( fun_int_int * int ) > int ).
tff(func_def_35,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(func_def_36,type,
hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(func_def_37,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(func_def_38,type,
hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(func_def_39,type,
hAPP_nat_real: ( fun_nat_real * nat ) > real ).
tff(func_def_40,type,
hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(func_def_41,type,
hAPP_real_bool: ( fun_real_bool * real ) > bool ).
tff(func_def_42,type,
hAPP_real_real: ( fun_real_real * real ) > real ).
tff(func_def_43,type,
hAPP_r1134773055l_bool: ( fun_re413263731l_bool * real ) > fun_real_bool ).
tff(func_def_44,type,
m1: int ).
tff(func_def_45,type,
n: nat ).
tff(func_def_46,type,
t: int ).
tff(func_def_47,type,
tn: nat ).
tff(func_def_48,type,
sK0: int > nat ).
tff(func_def_49,type,
sK1: int > nat ).
tff(func_def_50,type,
sK2: int > nat ).
tff(func_def_51,type,
sK3: int > nat ).
tff(func_def_52,type,
sK4: fun_int_bool > nat ).
tff(func_def_53,type,
sK5: fun_int_bool > int ).
tff(func_def_54,type,
sK6: fun_int_bool > int ).
tff(func_def_55,type,
sK7: fun_int_bool > nat ).
tff(func_def_56,type,
sK8: ( nat * fun_nat_bool ) > nat ).
tff(func_def_57,type,
sK9: ( nat * fun_nat_bool ) > nat ).
tff(func_def_58,type,
sK10: ( real * real ) > real ).
tff(func_def_59,type,
sK11: ( real * nat ) > real ).
tff(func_def_60,type,
sK12: ( real * nat ) > real ).
tff(func_def_61,type,
sK13: ( nat * nat ) > nat ).
tff(func_def_62,type,
sK14: ( nat * nat ) > nat ).
tff(func_def_63,type,
sK15: ( int * int ) > nat ).
tff(func_def_64,type,
sK16: ( fun_int_bool * int ) > int ).
tff(func_def_65,type,
sK17: ( fun_int_bool * int ) > int ).
tff(func_def_66,type,
sK18: fun_nat_nat > nat ).
tff(func_def_67,type,
sK19: fun_nat_nat > nat ).
tff(func_def_68,type,
sK20: fun_nat_nat > nat ).
tff(func_def_69,type,
sK21: fun_nat_nat > nat ).
tff(pred_def_1,type,
hBOOL: bool > $o ).
tff(f3215,plain,
$false,
inference(subsumption_resolution,[],[f3214,f2063]) ).
tff(f2063,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox/tmp/tmp.t6alYAMRYW/Vampire---4.8_17630',fact_0_n1pos) ).
tff(f3214,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(subsumption_resolution,[],[f3151,f3045]) ).
tff(f3045,plain,
! [X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(equality_resolution,[],[f2567]) ).
tff(f2567,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f1853]) ).
tff(f1853,plain,
! [X0: int,X1: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ( X0 = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
& ( ( ( X0 != X1 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
inference(flattening,[],[f1852]) ).
tff(f1852,plain,
! [X0: int,X1: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ( X0 = X1 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
& ( ( ( X0 != X1 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
inference(nnf_transformation,[],[f1048]) ).
tff(f1048,plain,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
<=> ( ( X0 != X1 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
inference(rectify,[],[f448]) ).
tff(f448,axiom,
! [X27: int,X22: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X27),X22))
<=> ( ( X22 != X27 )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X27),X22)) ) ),
file('/export/starexec/sandbox/tmp/tmp.t6alYAMRYW/Vampire---4.8_17630',fact_447_zless__le) ).
tff(f3151,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(superposition,[],[f2452,f3119]) ).
tff(f3119,plain,
zero_zero_int = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(zero_zero_int)))),
inference(forward_demodulation,[],[f1977,f1986]) ).
tff(f1986,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
zero_zero_int = pls,
file('/export/starexec/sandbox/tmp/tmp.t6alYAMRYW/Vampire---4.8_17630',fact_98_Pls__def) ).
tff(f1977,plain,
zero_zero_int = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f705]) ).
tff(f705,plain,
zero_zero_int = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f704]) ).
tff(f704,negated_conjecture,
( ~ zero_zero_int != hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) ),
inference(negated_conjecture,[],[f703]) ).
tff(f703,conjecture,
zero_zero_int != hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox/tmp/tmp.t6alYAMRYW/Vampire---4.8_17630',conj_0) ).
tff(f2452,plain,
! [X0: nat,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f1389]) ).
tff(f1389,plain,
! [X0: nat,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(ennf_transformation,[],[f978]) ).
tff(f978,plain,
! [X0: nat,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X0))) ),
inference(rectify,[],[f268]) ).
tff(f268,axiom,
! [X75: nat,X76: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X76))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X76),X75))) ),
file('/export/starexec/sandbox/tmp/tmp.t6alYAMRYW/Vampire---4.8_17630',fact_267_zero__less__power) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.17 % Problem : NUM925_2 : TPTP v8.1.2. Released v5.3.0.
% 0.10/0.18 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.18/0.38 % Computer : n032.cluster.edu
% 0.18/0.38 % Model : x86_64 x86_64
% 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38 % Memory : 8042.1875MB
% 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38 % CPULimit : 300
% 0.18/0.38 % WCLimit : 300
% 0.18/0.38 % DateTime : Fri Aug 25 15:11:43 EDT 2023
% 0.18/0.38 % CPUTime :
% 0.18/0.38 This is a TF0_THM_EQU_NAR problem
% 0.18/0.39 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.t6alYAMRYW/Vampire---4.8_17630
% 0.18/0.39 % (17741)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.46 % (17742)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_1064 on Vampire---4 for (1064ds/0Mi)
% 0.25/0.47 % (17743)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_957 on Vampire---4 for (957ds/0Mi)
% 0.25/0.47 % (17746)lrs+1002_9_av=off:bs=on:bsr=on:bce=on:cond=on:drc=off:er=filter:flr=on:fsd=off:fsr=off:fde=unused:lcm=predicate:nm=2:nwc=1.3:sims=off:stl=62_466 on Vampire---4 for (466ds/0Mi)
% 0.25/0.47 % (17745)dis-1010_4:3_afr=on:amm=off:bsr=on:bce=on:drc=off:fsd=off:fde=unused:gs=on:gsaa=from_current:irw=on:nwc=1.3:nicw=on:sas=z3:tgt=full:urr=ec_only_619 on Vampire---4 for (619ds/0Mi)
% 0.25/0.47 % (17747)ott+10_8_br=off:cond=on:fsr=off:gsp=on:nm=16:nwc=3.0:sims=off:sp=reverse_frequency:urr=on_432 on Vampire---4 for (432ds/0Mi)
% 0.25/0.47 % (17748)dis+1011_3:2_av=off:ep=RST:fsd=off:fde=none:gsp=on:nm=2:nwc=2.0:sos=on:sp=reverse_frequency_405 on Vampire---4 for (405ds/0Mi)
% 0.25/0.47 % (17744)lrs+1010_4_aac=none:add=off:afr=on:amm=off:anc=all_dependent:bd=off:cond=on:drc=off:flr=on:fde=none:gs=on:lma=on:nm=16:nwc=1.1:sims=off:sos=all:sac=on:sp=occurrence:stl=188_669 on Vampire---4 for (669ds/0Mi)
% 0.25/0.50 % (17744)First to succeed.
% 0.25/0.51 % (17744)Refutation found. Thanks to Tanya!
% 0.25/0.51 % SZS status Theorem for Vampire---4
% 0.25/0.51 % SZS output start Proof for Vampire---4
% See solution above
% 0.25/0.51 % (17744)------------------------------
% 0.25/0.51 % (17744)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.25/0.51 % (17744)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.25/0.51 % (17744)Termination reason: Refutation
% 0.25/0.51
% 0.25/0.51 % (17744)Memory used [KB]: 12920
% 0.25/0.51 % (17744)Time elapsed: 0.032 s
% 0.25/0.51 % (17744)------------------------------
% 0.25/0.51 % (17744)------------------------------
% 0.25/0.51 % (17741)Success in time 0.116 s
% 0.25/0.51 17745 Aborted by signal SIGHUP on /export/starexec/sandbox/tmp/tmp.t6alYAMRYW/Vampire---4.8_17630
% 0.25/0.51 % (17745)------------------------------
% 0.25/0.51 % (17745)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.25/0.51 % (17745)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.25/0.51 % (17745)Termination reason: Unknown
% 0.25/0.51 % (17745)Termination phase: Saturation
% 0.25/0.51
% 0.25/0.51 % (17745)Memory used [KB]: 7547
% 0.25/0.51 % (17745)Time elapsed: 0.038 s
% 0.25/0.51 % (17745)------------------------------
% 0.25/0.51 % (17745)------------------------------
% 0.25/0.51 % Vampire---4.8 exiting
%------------------------------------------------------------------------------