%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM080_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 : n014.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 09:40:16 AM UTC 2026
% Result : Theorem 0.19s 0.32s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 3 |; 1 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 15 ( 14 !; 1 ?; 15 :)
% 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: int ).
tff(func_def_32,type,
sK1: list(int) ).
tff(func_def_33,type,
sK2: int ).
tff(func_def_34,type,
sK3: int ).
tff(func_def_35,type,
sK4:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_36,type,
sK5: ( list(int) * list(fm(atom)) ) > fm(atom) ).
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(X0) > X0 ) ).
tff(func_def_40,type,
sK9:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_41,type,
sK10: ( list(int) * list(fm(atom)) ) > fm(atom) ).
tff(func_def_42,type,
sK11:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) * X0 ) > X0 ) ).
tff(func_def_43,type,
sK12:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_44,type,
sK13:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_45,type,
sK14:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_46,type,
sK15:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_47,type,
sK16:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_48,type,
sK17:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(func_def_49,type,
sK18: atom ).
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(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/sandbox2/benchmark/theBenchmark.p',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(f5,axiom,
! [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))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_IZ__asubst) ).
tff(f123,conjecture,
! [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))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f124,negated_conjecture,
~ ! [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(negated_conjecture,[status(cth)],[f123]) ).
tff(f125,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(f128,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,[],[f125]) ).
tff(f195,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,[],[f124]) ).
tff(f196,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,[],[f128]) ).
tff(f201,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,[],[f5]) ).
tff(f356,plain,
member(atom,sK18,set(atom,as)),
inference(cnf_transformation,[],[f195]) ).
tff(f357,plain,
~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK18),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,[],[f195]) ).
tff(f1424,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),sK18)),xs)),
inference(resolution,[],[f201,f357]) ).
tff(f1436,plain,
~ member(atom,sK18,set(atom,as)),
inference(resolution,[],[f1424,f196]) ).
tff(f1438,plain,
$false,
inference(forward_subsumption_resolution,[],[f1436,f356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM080_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n014.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 21:53:00 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 0.19/0.32 % (2219155)Will run a generic schedule for satisfiability detection.
% 0.19/0.32 % (2219164)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2557472977:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.32 % (2219161)% WARNING: option uhcvi not known.
% 0.19/0.32 % (2219163)dis+10_1_sil=32000:sp=arity:random_seed=624258821:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.32 % (2219160)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3776287386_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.32 % (2219161)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2147299034:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.32 % (2219162)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1607416067:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.32 % (2219165)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4108775028:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.32 % (2219166)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3642990567:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.32 % Exception at run slice level
% 0.19/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.32 % (2219164) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2219155-2219164"...
% 0.19/0.32 % (2219164)...printing done.
% 0.19/0.32 % (2219161) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2219155-2219161"...
% 0.19/0.32 % (2219164)Refutation found. Thanks to Tanya!
% 0.19/0.32 % SZS status Theorem for theBenchmark
% 0.19/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.32 % (2219164)------------------------------
% 0.19/0.32 % (2219164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (2219164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (2219164)CaDiCaL version: 2.1.3
% 0.19/0.32 % (2219164)Termination reason: Refutation
% 0.19/0.32 % (2219164)Time elapsed: 0.037 s
% 0.19/0.32 % (2219164)Peak memory usage: 13 MB
% 0.19/0.32 % (2219164)Instructions burned: 98 (million)
% 0.19/0.32 % (2219155)Success in time 0.083 s
% 0.19/0.32 % Vampire exiting
%------------------------------------------------------------------------------