%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL809_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:00:41 PM UTC 2026
% Result : Theorem 0.35s 0.48s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 55 ( 55 usr; 15 con; 0-5 aty)
% Number of variables : 22 ( 22 !; 0 ?; 22 :)
% 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,
char1: $tType ).
tff(type_def_10,type,
literal: $tType ).
tff(type_def_11,type,
nibble: $tType ).
tff(type_def_12,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_3,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_4,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_5,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_6,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_7,type,
bool_size: bool > nat ).
tff(func_def_8,type,
it: fun(dB,bool) ).
tff(func_def_9,type,
abs: dB > dB ).
tff(func_def_10,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_11,type,
var: nat > dB ).
tff(func_def_12,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_13,type,
dB_size: dB > nat ).
tff(func_def_14,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_15,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_16,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_17,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_18,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_19,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_20,type,
monoid_add_listsum:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_21,type,
suc: nat > nat ).
tff(func_def_22,type,
nat_size: nat > nat ).
tff(func_def_23,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_24,type,
char: ( nibble * nibble ) > char1 ).
tff(func_def_25,type,
char_case:
!>[X0: $tType] : ( ( fun(nibble,fun(nibble,X0)) * char1 ) > X0 ) ).
tff(func_def_26,type,
char_rec:
!>[X0: $tType] : ( ( fun(nibble,fun(nibble,X0)) * char1 ) > X0 ) ).
tff(func_def_27,type,
char_size: char1 > nat ).
tff(func_def_28,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_29,type,
fFalse: bool ).
tff(func_def_30,type,
fTrue: bool ).
tff(func_def_31,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_32,type,
a: dB ).
tff(func_def_33,type,
b: dB ).
tff(func_def_34,type,
bs: list(dB) ).
tff(func_def_35,type,
i: nat ).
tff(func_def_36,type,
n: nat ).
tff(func_def_37,type,
t: dB ).
tff(func_def_38,type,
u: dB ).
tff(func_def_39,type,
ua: dB ).
tff(func_def_40,type,
sK0: char1 > nibble ).
tff(func_def_41,type,
sK1: char1 > nibble ).
tff(func_def_42,type,
sK2:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_43,type,
sK3: dB > dB ).
tff(func_def_44,type,
sK4: dB > dB ).
tff(func_def_45,type,
sK5: dB > list(dB) ).
tff(func_def_46,type,
sK6: dB > dB ).
tff(func_def_47,type,
sK7: dB > list(dB) ).
tff(func_def_48,type,
sK8: dB > nat ).
tff(func_def_49,type,
sK9: nat > nat ).
tff(func_def_50,type,
sK10: fun(nat,bool) > nat ).
tff(func_def_51,type,
sK11: nat > nat ).
tff(func_def_52,type,
sK12: fun(nat,bool) > nat ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_6,type,
pp: bool > $o ).
tff(f4,axiom,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096IT_A_Ib_091u_Pi_093_J_096) ).
tff(f5,axiom,
n = i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_True) ).
tff(f6,axiom,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_lift__IT) ).
tff(f105,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f116,conjecture,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i)),zero_zero(nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f117,negated_conjecture,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i)),zero_zero(nat)))),
inference(negated_conjecture,[status(cth)],[f116]) ).
tff(f119,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i)),zero_zero(nat)))),
inference(flattening,[],[f117]) ).
tff(f121,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f6]) ).
tff(f145,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i))),
inference(cnf_transformation,[],[f4]) ).
tff(f146,plain,
i = n,
inference(cnf_transformation,[],[f5]) ).
tff(f147,plain,
! [X0: nat,X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) ),
inference(cnf_transformation,[],[f121]) ).
tff(f280,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f105]) ).
tff(f291,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i)),zero_zero(nat)))),
inference(cnf_transformation,[],[f119]) ).
tff(f292,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n))),
inference(definition_unfolding,[],[f145,f146]) ).
tff(f299,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n)),zero_zero(nat)))),
inference(definition_unfolding,[],[f291,f146]) ).
tff(f324,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n))),
inference(consistent_polarity_flipping,[],[f292]) ).
tff(f325,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) ),
inference(consistent_polarity_flipping,[],[f147]) ).
tff(f362,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n)),zero_zero(nat)))),
inference(consistent_polarity_flipping,[],[f299]) ).
tff(f782,plain,
pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n)))),
inference(superposition,[],[f362,f280]) ).
tff(f793,plain,
pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,b),n),u)))),
inference(forward_demodulation,[],[f782,f280]) ).
tff(f829,plain,
! [X0: nat,X1: dB] :
( ~ pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))
| pp(aa(dB,bool,it,X1)) ),
inference(forward_demodulation,[],[f325,f280]) ).
tff(f831,plain,
pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,b),n),u))),
inference(resolution,[],[f829,f793]) ).
tff(f927,plain,
~ pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,b),n),u))),
inference(forward_demodulation,[],[f324,f280]) ).
tff(f928,plain,
$false,
inference(forward_subsumption_resolution,[],[f927,f831]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL809_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 16:53:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/0.48 % (2248965)Will run a generic schedule for satisfiability detection.
% 0.35/0.48 % (2248975)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1545846022:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.35/0.48 % (2248971)% WARNING: option uhcvi not known.
% 0.35/0.48 % (2248970)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1536618400_2999 on theBenchmark for (2999ds/0Mi)
% 0.35/0.48 % (2248971)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=629297477:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.35/0.48 % (2248972)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1254371060:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.35/0.48 % (2248973)dis+10_1_sil=32000:sp=arity:random_seed=1169709151:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.35/0.48 % (2248976)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2245423374:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.35/0.48 % (2248974)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=266348271:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.35/0.48 % Exception at run slice level
% 0.35/0.48 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.35/0.48 % (2248984)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2413500744:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.35/0.48 % Exception at run slice level
% 0.35/0.48 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.35/0.48 % (2248971) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2248965-2248971"...
% 0.35/0.48 % (2248971)...printing done.
% 0.35/0.48 % (2248971)Refutation found. Thanks to Tanya!
% 0.35/0.48 % SZS status Theorem for theBenchmark
% 0.35/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.48 % (2248971)------------------------------
% 0.35/0.48 % (2248971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.48 % (2248971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.48 % (2248971)CaDiCaL version: 2.1.3
% 0.35/0.48 % (2248971)Termination reason: Refutation
% 0.35/0.48 % (2248971)Time elapsed: 0.031 s
% 0.35/0.48 % (2248971)Peak memory usage: 12 MB
% 0.35/0.48 % (2248971)Instructions burned: 47 (million)
% 0.35/0.48 % (2248965)Success in time 0.07 s
% 0.35/0.48 % Vampire exiting
%------------------------------------------------------------------------------