%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL813_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 12:00:42 PM UTC 2026
% Result : Theorem 0.17s 0.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 4 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 66 ( 66 usr; 26 con; 0-5 aty)
% Number of variables : 47 ( 47 !; 0 ?; 47 :)
% 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(X0,fun1(X1,X2)) * 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] : ( ( X0 * 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,
map:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_17,type,
shift:
!>[X0: $tType] : ( ( fun1(nat,X0) * nat * X0 ) > fun1(nat,X0) ) ).
tff(func_def_18,type,
fun: fun1(type,fun1(type,type)) ).
tff(func_def_19,type,
typing: fun1(nat,type) > fun1(dB,fun1(type,bool)) ).
tff(func_def_20,type,
typings: ( fun1(nat,type) * list(dB) ) > fun1(list(type),bool) ).
tff(func_def_21,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,X1) * X0 ) > X1 ) ).
tff(func_def_22,type,
fEx:
!>[X0: $tType] : fun1(fun1(X0,bool),bool) ).
tff(func_def_23,type,
fFalse: bool ).
tff(func_def_24,type,
fTrue: bool ).
tff(func_def_25,type,
fconj: fun1(bool,fun1(bool,bool)) ).
tff(func_def_26,type,
t2: type ).
tff(func_def_27,type,
t: type ).
tff(func_def_28,type,
t_a: type ).
tff(func_def_29,type,
t1: type ).
tff(func_def_30,type,
ts: list(type) ).
tff(func_def_31,type,
a: dB ).
tff(func_def_32,type,
as: list(dB) ).
tff(func_def_33,type,
e: fun1(nat,type) ).
tff(func_def_34,type,
ea: fun1(nat,type) ).
tff(func_def_35,type,
i: nat ).
tff(func_def_36,type,
ia: nat ).
tff(func_def_37,type,
n: nat ).
tff(func_def_38,type,
rs: list(dB) ).
tff(func_def_39,type,
t3: dB ).
tff(func_def_40,type,
u: dB ).
tff(func_def_41,type,
ua: dB ).
tff(func_def_42,type,
sK0: ( type * dB * fun1(nat,type) ) > type ).
tff(func_def_43,type,
sK1: ( type * dB * fun1(nat,type) ) > type ).
tff(func_def_44,type,
sK2: type ).
tff(func_def_45,type,
sK3: ( dB * fun1(nat,type) ) > type ).
tff(func_def_46,type,
sK4: ( dB * fun1(nat,type) ) > type ).
tff(func_def_47,type,
sK5: list(type) ).
tff(func_def_48,type,
sK6: ( type * dB * dB * fun1(nat,type) ) > type ).
tff(func_def_49,type,
sK7: ( type * list(dB) * nat * fun1(nat,type) ) > list(type) ).
tff(func_def_50,type,
sK8: ( type * type * list(dB) * fun1(nat,type) ) > list(type) ).
tff(func_def_51,type,
sK9: ( type * list(dB) * dB * fun1(nat,type) ) > list(type) ).
tff(func_def_52,type,
sK10: ( type * list(dB) * dB * fun1(nat,type) ) > list(type) ).
tff(func_def_53,type,
sK11:
!>[X0: $tType,X1: $tType] : ( ( fun1(X1,X0) * fun1(X1,X0) ) > X1 ) ).
tff(func_def_54,type,
sK12: ( dB * dB ) > dB ).
tff(func_def_55,type,
sK13: dB > dB ).
tff(func_def_56,type,
sK14: dB > dB ).
tff(func_def_57,type,
sK15: dB > list(dB) ).
tff(func_def_58,type,
sK16: dB > dB ).
tff(func_def_59,type,
sK17: dB > list(dB) ).
tff(func_def_60,type,
sK18: dB > nat ).
tff(func_def_61,type,
sK19: ( dB * dB * dB ) > dB ).
tff(func_def_62,type,
sK20: ( dB * dB * dB ) > dB ).
tff(func_def_63,type,
sK21: ( dB * dB * dB ) > dB ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
beta: ( dB * dB ) > $o ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun1(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(f2,axiom,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_typing_OVar) ).
tff(f11,axiom,
! [X0: $tType,X1: X0,X2: fun1(nat,X0),X3: nat,X4: nat] :
( ( X4 = X3 )
=> ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_shift__eq) ).
tff(f105,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun1(X0,fun1(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f113,conjecture,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f114,negated_conjecture,
~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t))),
inference(negated_conjecture,[status(cth)],[f113]) ).
tff(f117,plain,
~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t))),
inference(flattening,[],[f114]) ).
tff(f118,plain,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f120,plain,
! [X0: $tType,X1: X0,X2: fun1(nat,X0),X3: nat,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f171,plain,
! [X2: fun1(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) != X0 )
| pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0)) ),
inference(cnf_transformation,[],[f118]) ).
tff(f183,plain,
! [X0: $tType,X2: fun1(nat,X0),X3: nat,X1: X0,X4: nat] :
( ( X3 != X4 )
| ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 ) ),
inference(cnf_transformation,[],[f120]) ).
tff(f319,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun1(X0,fun1(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f105]) ).
tff(f327,plain,
~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t))),
inference(cnf_transformation,[],[f117]) ).
tff(f343,plain,
! [X2: fun1(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1))),
inference(equality_resolution,[],[f171]) ).
tff(f347,plain,
! [X0: $tType,X2: fun1(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ),
inference(equality_resolution,[],[f183]) ).
tff(f445,plain,
! [X2: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1))),
inference(forward_demodulation,[],[f343,f319]) ).
tff(f1142,plain,
! [X2: nat,X0: type,X1: fun1(nat,type)] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X1,X2,X0)),X0),var(X2))),
inference(superposition,[],[f445,f347]) ).
tff(f1491,plain,
~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),foldr(type,type,fun,ts,t)),var(zero_zero(nat)))),
inference(superposition,[],[f327,f319]) ).
tff(f1493,plain,
$false,
inference(forward_subsumption_resolution,[],[f1491,f1142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL813_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 16:54:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.50 % (3171055)Will run a generic schedule for satisfiability detection.
% 0.17/0.50 % (3171060)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3850180224_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.50 % Exception at run slice level
% 0.17/0.50 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.50 % (3171061)% WARNING: option uhcvi not known.
% 0.17/0.50 % (3171061)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1474943469:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.50 % (3171062)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1481719371:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.50 % (3171063)dis+10_1_sil=32000:sp=arity:random_seed=2926245517:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.50 % (3171064)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3878008017:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.50 % (3171066)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3328315995:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.50 % (3171065)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1342246647:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.50 % (3171068)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1921631045:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.17/0.50 % Exception at run slice level
% 0.17/0.50 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.50 % (3171076)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=645811421:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.50 % (3171064) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3171055-3171064"...
% 0.17/0.50 % (3171064)...printing done.
% 0.17/0.50 % (3171064)Refutation found. Thanks to Tanya!
% 0.17/0.50 % SZS status Theorem for theBenchmark
% 0.17/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50 % (3171064)------------------------------
% 0.17/0.50 % (3171064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (3171064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (3171064)CaDiCaL version: 2.1.3
% 0.17/0.50 % (3171064)Termination reason: Refutation
% 0.17/0.50 % (3171064)Time elapsed: 0.043 s
% 0.17/0.50 % (3171064)Peak memory usage: 12 MB
% 0.17/0.50 % (3171064)Instructions burned: 75 (million)
% 0.17/0.50 % (3171055)Success in time 0.089 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------