%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL818_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:56:43 AM UTC 2026
% Result : Theorem 2.30s 1.16s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 71 ( 71 usr; 26 con; 0-6 aty)
% Number of variables : 21 ( 21 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
dB: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
type: $tType ).
tff(type_def_10,type,
fun1: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun1(fun1(X0,X1),fun1(fun1(X2,X0),fun1(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun1(X0,fun1(X1,X2)) * X1 ) > fun1(X0,X2) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun1(X0,X0) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : fun1(fun1(X0,fun1(X1,X2)),fun1(fun1(X0,X1),fun1(X0,X2))) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
it: fun1(dB,bool) ).
tff(func_def_6,type,
abs: dB > dB ).
tff(func_def_7,type,
app: fun1(dB,fun1(dB,dB)) ).
tff(func_def_8,type,
var: nat > dB ).
tff(func_def_9,type,
dB_size: dB > nat ).
tff(func_def_10,type,
lift: fun1(dB,fun1(nat,dB)) ).
tff(func_def_11,type,
subst: fun1(dB,fun1(dB,fun1(nat,dB))) ).
tff(func_def_12,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,fun1(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_13,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,fun1(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_14,type,
cons:
!>[X0: $tType] : fun1(X0,fun1(list(X0),list(X0))) ).
tff(func_def_15,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun1(X1,fun1(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_16,type,
listset:
!>[X0: $tType] : ( list(fun1(X0,bool)) > fun1(list(X0),bool) ) ).
tff(func_def_17,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_18,type,
set_Cons:
!>[X0: $tType] : ( ( fun1(X0,bool) * fun1(list(X0),bool) ) > fun1(list(X0),bool) ) ).
tff(func_def_19,type,
collect:
!>[X0: $tType] : ( fun1(X0,bool) > fun1(X0,bool) ) ).
tff(func_def_20,type,
shift:
!>[X0: $tType] : ( ( fun1(nat,X0) * nat * X0 ) > fun1(nat,X0) ) ).
tff(func_def_21,type,
fun: fun1(type,fun1(type,type)) ).
tff(func_def_22,type,
typing: fun1(nat,type) > fun1(dB,fun1(type,bool)) ).
tff(func_def_23,type,
typings: ( fun1(nat,type) * list(dB) ) > fun1(list(type),bool) ).
tff(func_def_24,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,X1) * X0 ) > X1 ) ).
tff(func_def_25,type,
fEx:
!>[X0: $tType] : fun1(fun1(X0,bool),bool) ).
tff(func_def_26,type,
fFalse: bool ).
tff(func_def_27,type,
fTrue: bool ).
tff(func_def_28,type,
fconj: fun1(bool,fun1(bool,bool)) ).
tff(func_def_29,type,
fequal:
!>[X0: $tType] : fun1(X0,fun1(X0,bool)) ).
tff(func_def_30,type,
member:
!>[X0: $tType] : fun1(X0,fun1(fun1(X0,bool),bool)) ).
tff(func_def_31,type,
t2: type ).
tff(func_def_32,type,
t: type ).
tff(func_def_33,type,
t_a: type ).
tff(func_def_34,type,
t1: type ).
tff(func_def_35,type,
ts: list(type) ).
tff(func_def_36,type,
a: dB ).
tff(func_def_37,type,
as: list(dB) ).
tff(func_def_38,type,
e: fun1(nat,type) ).
tff(func_def_39,type,
ea: fun1(nat,type) ).
tff(func_def_40,type,
i: nat ).
tff(func_def_41,type,
ia: nat ).
tff(func_def_42,type,
n: nat ).
tff(func_def_43,type,
rs: list(dB) ).
tff(func_def_44,type,
t3: dB ).
tff(func_def_45,type,
u: dB ).
tff(func_def_46,type,
ua: dB ).
tff(func_def_47,type,
sK1: ( type * dB * dB * fun1(nat,type) ) > type ).
tff(func_def_48,type,
sK2: type ).
tff(func_def_49,type,
sK3: list(type) ).
tff(func_def_50,type,
sK4: ( type * dB * fun1(nat,type) ) > type ).
tff(func_def_51,type,
sK5: ( type * dB * fun1(nat,type) ) > type ).
tff(func_def_52,type,
sK6: ( type * list(dB) * nat * fun1(nat,type) ) > list(type) ).
tff(func_def_53,type,
sK7: ( type * type * list(dB) * fun1(nat,type) ) > list(type) ).
tff(func_def_54,type,
sK8: ( type * list(dB) * dB * fun1(nat,type) ) > list(type) ).
tff(func_def_55,type,
sK9: ( type * list(dB) * dB * fun1(nat,type) ) > list(type) ).
tff(func_def_56,type,
sK10: ( dB * fun1(nat,type) ) > type ).
tff(func_def_57,type,
sK11: ( dB * fun1(nat,type) ) > type ).
tff(func_def_58,type,
sK12:
!>[X0: $tType,X1: $tType] : ( ( fun1(X1,X0) * fun1(X1,X0) ) > X1 ) ).
tff(func_def_59,type,
sK13:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun1(X0,X1) ) > X0 ) ).
tff(func_def_60,type,
sK14:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun1(X0,X1) ) > list(X0) ) ).
tff(func_def_61,type,
sK15: dB > dB ).
tff(func_def_62,type,
sK16: dB > dB ).
tff(func_def_63,type,
sK17: dB > list(dB) ).
tff(func_def_64,type,
sK18: dB > list(dB) ).
tff(func_def_65,type,
sK19: dB > nat ).
tff(func_def_66,type,
sK20: dB > dB ).
tff(func_def_67,type,
sK21:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun1(X1,X0) * list(X0) * X0 ) > X1 ) ).
tff(func_def_68,type,
sK22:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun1(X1,X0) * list(X0) * X0 ) > list(X1) ) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
listsp:
!>[X0: $tType] : ( ( fun1(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_3,type,
pp: bool > $o ).
tff(pred_def_4,type,
sP0: dB > $o ).
tff(pred_def_5,type,
sQ23_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f3,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),i)),t2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096e_A_092_060turnstile_062_Aa_091u_Pi_093_A_058_AT_H_H_096) ).
tff(f4,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),aa(type,type,aa(type,fun1(type,type),fun,t2),foldr(type,type,fun,ts,t)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_uT_H) ).
tff(f8,axiom,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1)))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_App) ).
tff(f115,conjecture,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),aa(dB,dB,aa(dB,fun1(dB,dB),app,u),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),i))),foldr(type,type,fun,ts,t))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f116,negated_conjecture,
~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),aa(dB,dB,aa(dB,fun1(dB,dB),app,u),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),i))),foldr(type,type,fun,ts,t))),
inference(negated_conjecture,[status(cth)],[f115]) ).
tff(f118,plain,
~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),aa(dB,dB,aa(dB,fun1(dB,dB),app,u),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),i))),foldr(type,type,fun,ts,t))),
inference(flattening,[],[f116]) ).
tff(f119,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ),
inference(ennf_transformation,[],[f8]) ).
tff(f120,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ),
inference(flattening,[],[f119]) ).
tff(f205,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),i)),t2)),
inference(cnf_transformation,[],[f3]) ).
tff(f206,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),aa(type,type,aa(type,fun1(type,type),fun,t2),foldr(type,type,fun,ts,t)))),
inference(cnf_transformation,[],[f4]) ).
tff(f210,plain,
! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ),
inference(cnf_transformation,[],[f120]) ).
tff(f359,plain,
~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),aa(dB,dB,aa(dB,fun1(dB,dB),app,u),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),i))),foldr(type,type,fun,ts,t))),
inference(cnf_transformation,[],[f118]) ).
tff(f1035,plain,
! [X0: type] :
( ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),i)),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),aa(type,type,aa(type,fun1(type,type),fun,X0),foldr(type,type,fun,ts,t)))) ),
inference(resolution,[],[f210,f359]) ).
tff(f1039,plain,
~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),aa(type,type,aa(type,fun1(type,type),fun,t2),foldr(type,type,fun,ts,t)))),
inference(resolution,[],[f1035,f205]) ).
tff(f1042,plain,
$false,
inference(resolution,[],[f1039,f206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL818_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 16:58:30 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.30/1.16 % (1854350)Detected formulas, will run a generic FOF schedule.
% 2.30/1.16 % (1854361)dis-21_1_sil=8000:lcm=predicate:random_seed=661463304:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.30/1.16 % (1854361)First to succeed.
% 2.30/1.16 % (1854361)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1854350"
% 2.30/1.16 % (1854359)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2968803207:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.30/1.16 % (1854356)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2146688080:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.30/1.16 % (1854360)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2937741581:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.30/1.16 % (1854358)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=975998311:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.30/1.16 % (1854355)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2818638377:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.30/1.16 % (1854357)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=967850847:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.30/1.16 % (1854358)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.30/1.16 % (1854358)Refutation not found, incomplete strategy
% 2.30/1.16 % (1854358)------------------------------
% 2.30/1.16 % (1854358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.30/1.16 % (1854358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.16 % (1854358)CaDiCaL version: 2.1.3
% 2.30/1.16 % (1854358)Termination reason: Refutation not found, incomplete strategy
% 2.30/1.16 % (1854358)Time elapsed: 0.003 s
% 2.30/1.16 % (1854358)Peak memory usage: 88 MB
% 2.30/1.16 % (1854358)Instructions burned: 4 (million)
% 2.30/1.16 % (1854357)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.30/1.16 % (1854359)Instruction limit reached!
% 2.30/1.16 % (1854359)------------------------------
% 2.30/1.16 % (1854359)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.30/1.16 % (1854359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.16 % (1854359)CaDiCaL version: 2.1.3
% 2.30/1.16 % (1854359)Termination reason: Instruction limit
% 2.30/1.16 % (1854359)Termination phase: Saturation
% 2.30/1.16 % (1854359)Time elapsed: 0.070 s
% 2.30/1.16 % (1854359)Peak memory usage: 88 MB
% 2.30/1.16 % (1854359)Instructions burned: 120 (million)
% 2.30/1.16 % (1854360)Instruction limit reached!
% 2.30/1.16 % (1854360)------------------------------
% 2.30/1.16 % (1854360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.30/1.16 % (1854360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.16 % (1854360)CaDiCaL version: 2.1.3
% 2.30/1.16 % (1854360)Termination reason: Instruction limit
% 2.30/1.16 % (1854360)Termination phase: Saturation
% 2.30/1.16 % (1854360)Time elapsed: 0.078 s
% 2.30/1.16 % (1854360)Peak memory usage: 89 MB
% 2.30/1.16 % (1854360)Instructions burned: 139 (million)
% 2.30/1.16 % (1854361)Refutation found. Thanks to Tanya!
% 2.30/1.16 % SZS status Theorem for theBenchmark
% 2.30/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.33 % (1854361)------------------------------
% 2.73/1.33 % (1854361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.33 % (1854361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.33 % (1854361)CaDiCaL version: 2.1.3
% 2.73/1.33 % (1854361)Termination reason: Refutation
% 2.73/1.33 % (1854361)Time elapsed: 0.016 s
% 2.73/1.33 % (1854361)Peak memory usage: 89 MB
% 2.73/1.33 % (1854361)Instructions burned: 49 (million)
% 2.73/1.33 % (1854361)------------------------------
% 2.73/1.33 % (1854361)------------------------------
% 2.73/1.33 % (1854350)Success in time 0.309 s
% 2.73/1.33 % Vampire exiting
%------------------------------------------------------------------------------