TSTP Solution File: COM080_5 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : COM080_5 : TPTP v8.1.2. Released v6.0.0.
% 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 : n027.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 : Wed Aug 30 18:46:36 EDT 2023
% Result : Theorem 0.23s 0.46s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 78
% Syntax : Number of formulae : 93 ( 5 unt; 74 typ; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 13 ~; 5 |; 5 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 66 ( 43 >; 23 *; 0 +; 0 <<)
% Number of predicates : 17 ( 16 usr; 1 prp; 0-5 aty)
% Number of functors : 54 ( 54 usr; 13 con; 0-5 aty)
% Number of variables : 77 (; 23 !; 2 ?; 77 :)
% ( 52 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
fm: $tType > $tType ).
tff(type_def_9,type,
nat: $tType ).
tff(type_def_10,type,
atom: $tType ).
tff(type_def_11,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_12,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
plus_plus:
!>[X0: $tType] : fun(X0,fun(X0,X0)) ).
tff(func_def_1,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
iprod:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > X0 ) ).
tff(func_def_4,type,
zipwith0:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,fun(X1,X2)) > fun(list(X0),fun(list(X1),list(X2))) ) ).
tff(func_def_5,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_6,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_7,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_8,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_9,type,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
tff(func_def_10,type,
set:
!>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).
tff(func_def_11,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_13,type,
list_conj:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_14,type,
list_disj:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_15,type,
map_fm:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fm(X0) ) > fm(X1) ) ).
tff(func_def_16,type,
neg:
!>[X0: $tType] : ( fm(X0) > fm(X0) ) ).
tff(func_def_17,type,
suc: nat > nat ).
tff(func_def_18,type,
i_Z: fun(atom,fun(list(int),bool)) ).
tff(func_def_19,type,
asubst: ( int * list(int) ) > fun(atom,atom) ).
tff(func_def_20,type,
divisor: atom > int ).
tff(func_def_21,type,
lbounds: list(atom) > list(product_prod(int,list(int))) ).
tff(func_def_22,type,
qEpres896714165pres_1: list(atom) > fm(atom) ).
tff(func_def_23,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_24,type,
fFalse: bool ).
tff(func_def_25,type,
fTrue: bool ).
tff(func_def_26,type,
as: list(atom) ).
tff(func_def_27,type,
il: int ).
tff(func_def_28,type,
ksl: list(int) ).
tff(func_def_29,type,
m: int ).
tff(func_def_30,type,
xs: list(int) ).
tff(func_def_31,type,
sK0: atom ).
tff(func_def_32,type,
sK1: int ).
tff(func_def_33,type,
sK2: int ).
tff(func_def_34,type,
sK3: list(int) ).
tff(func_def_35,type,
sK4: int ).
tff(func_def_36,type,
sK5:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_37,type,
sK6:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_38,type,
sK7:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_39,type,
sK8:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_40,type,
sK9:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_41,type,
sK10:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_42,type,
sK11:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_43,type,
sK12: ( list(int) * list(fm(atom)) ) > fm(atom) ).
tff(func_def_44,type,
sK13: ( list(int) * list(fm(atom)) ) > fm(atom) ).
tff(func_def_45,type,
sK14:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_46,type,
sK15:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(func_def_47,type,
sK16:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_48,type,
sK17:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) * X0 ) > X0 ) ).
tff(func_def_49,type,
sK18:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
cl_Groups_Oplus:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_13,type,
interpret:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(list(X1),bool)) * fm(X0) * list(X1) ) > $o ) ).
tff(pred_def_14,type,
qfree:
!>[X0: $tType] : ( fm(X0) > $o ) ).
tff(pred_def_15,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_16,type,
pp: bool > $o ).
tff(f568,plain,
$false,
inference(subsumption_resolution,[],[f554,f539]) ).
tff(f539,plain,
pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),sK0)),xs)),
inference(resolution,[],[f352,f422]) ).
tff(f422,plain,
! [X0: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs))
| ~ member(atom,X0,set(atom,as)) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs))
| ~ member(atom,X0,set(atom,as)) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: atom] :
( member(atom,X0,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs)) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X4: atom] :
( member(atom,X4,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X4)),xs)) ),
file('/export/starexec/sandbox/tmp/tmp.EbZcv8Y2FG/Vampire---4.8_2598',fact_0__096ALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_A_Iasubst_A_Iil_A_L_Am_J_Aksl_Aa_J_Axs_096) ).
tff(f352,plain,
member(atom,sK0,set(atom,as)),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
& member(atom,sK0,set(atom,as)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f224,f292]) ).
tff(f292,plain,
( ? [X0: atom] :
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
& member(atom,X0,set(atom,as)) )
=> ( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
& member(atom,sK0,set(atom,as)) ) ),
introduced(choice_axiom,[]) ).
tff(f224,plain,
? [X0: atom] :
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
& member(atom,X0,set(atom,as)) ),
inference(ennf_transformation,[],[f125]) ).
tff(f125,plain,
~ ! [X0: atom] :
( member(atom,X0,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))) ),
inference(rectify,[],[f124]) ).
tff(f124,negated_conjecture,
~ ! [X22: atom] :
( member(atom,X22,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X22),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))) ),
inference(negated_conjecture,[],[f123]) ).
tff(f123,conjecture,
! [X22: atom] :
( member(atom,X22,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X22),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))) ),
file('/export/starexec/sandbox/tmp/tmp.EbZcv8Y2FG/Vampire---4.8_2598',conj_0) ).
tff(f554,plain,
~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),sK0)),xs)),
inference(resolution,[],[f353,f509]) ).
tff(f509,plain,
! [X2: list(int),X3: int,X0: list(int),X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0)))
| ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f349]) ).
tff(f349,plain,
! [X0: list(int),X1: atom,X2: list(int),X3: int] :
( ( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0))
| ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0))) )
& ( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0)))
| ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0)) ) ),
inference(nnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: list(int),X1: atom,X2: list(int),X3: int] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0))
<=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0))) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X12: list(int),X13: atom,X14: list(int),X15: int] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X15,X14),X13)),X12))
<=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X13),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X15),iprod(int,X14,X12)),X12))) ),
file('/export/starexec/sandbox/tmp/tmp.EbZcv8Y2FG/Vampire---4.8_2598',fact_4_IZ__asubst) ).
tff(f353,plain,
~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))),
inference(cnf_transformation,[],[f293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : COM080_5 : TPTP v8.1.2. Released v6.0.0.
% 0.00/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.17/0.37 % Computer : n027.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Tue Aug 29 13:15:38 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.17/0.38 This is a TF1_THM_EQU_NAR problem
% 0.17/0.38 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.EbZcv8Y2FG/Vampire---4.8_2598
% 0.17/0.38 % (2715)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.45 % (2722)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.23/0.45 % (2717)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.23/0.45 % (2718)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.23/0.45 % (2721)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_520 on Vampire---4 for (520ds/0Mi)
% 0.23/0.45 % (2720)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.45 % (2716)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.23/0.45 % (2719)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.23/0.45 % (2716)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.45 % (2719)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.46 % (2718)First to succeed.
% 0.23/0.46 % (2719)Also succeeded, but the first one will report.
% 0.23/0.46 % (2718)Refutation found. Thanks to Tanya!
% 0.23/0.46 % SZS status Theorem for Vampire---4
% 0.23/0.46 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.46 % (2718)------------------------------
% 0.23/0.46 % (2718)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.46 % (2718)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.46 % (2718)Termination reason: Refutation
% 0.23/0.46
% 0.23/0.46 % (2718)Memory used [KB]: 10618
% 0.23/0.46 % (2718)Time elapsed: 0.016 s
% 0.23/0.46 % (2718)------------------------------
% 0.23/0.46 % (2718)------------------------------
% 0.23/0.47 % (2715)Success in time 0.082 s
% 0.23/0.47 % Vampire---4.8 exiting
%------------------------------------------------------------------------------