%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM088_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 09:39:32 AM UTC 2026
% Result : Theorem 4.09s 1.63s
% Output : Refutation 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 14 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 50 ( 50 usr; 8 con; 0-5 aty)
% Number of variables : 16 ( 16 !; 0 ?; 16 :)
% 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,
nat: $tType ).
tff(type_def_9,type,
atom: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_11,type,
product_prod: ( $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,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
minus_minus:
!>[X0: $tType] : fun(X0,fun(X0,X0)) ).
tff(func_def_5,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_6,type,
iprod:
!>[X0: $tType] : fun(list(X0),fun(list(X0),X0)) ).
tff(func_def_7,type,
zipwith0:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,fun(X1,X2)) > fun(list(X0),fun(list(X1),list(X2))) ) ).
tff(func_def_8,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_9,type,
linord2118332866rt_key:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 * list(X0) ) > list(X0) ) ).
tff(func_def_10,type,
linorder_insort_key:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 * list(X0) ) > list(X0) ) ).
tff(func_def_11,type,
linorder_sort_key:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_13,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_14,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_15,type,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
tff(func_def_16,type,
set:
!>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).
tff(func_def_17,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_18,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_19,type,
divisor: atom > int ).
tff(func_def_20,type,
lbounds: list(atom) > list(product_prod(int,list(int))) ).
tff(func_def_21,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_22,type,
product_prod_case:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_23,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_24,type,
image:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fun(X0,bool) ) > fun(X1,bool) ) ).
tff(func_def_25,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_26,type,
fFalse: bool ).
tff(func_def_27,type,
fNot: fun(bool,bool) ).
tff(func_def_28,type,
fTrue: bool ).
tff(func_def_29,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_30,type,
fdisj: fun(bool,fun(bool,bool)) ).
tff(func_def_31,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_32,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_33,type,
as: list(atom) ).
tff(func_def_34,type,
x: int ).
tff(func_def_35,type,
xs: list(int) ).
tff(func_def_36,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,bool) ) > X1 ) ).
tff(func_def_37,type,
sK1:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_38,type,
sK2:
!>[X0: $tType] : ( fun(X0,bool) > list(X0) ) ).
tff(func_def_39,type,
sK3:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) * fun(X1,bool) ) > X1 ) ).
tff(func_def_40,type,
sK4:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,bool) * fun(X1,X0) * X0 ) > X1 ) ).
tff(func_def_41,type,
sK5:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,bool) * fun(X1,X0) * X0 ) > X1 ) ).
tff(func_def_42,type,
sK6:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_43,type,
sK7:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_44,type,
sK8:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_45,type,
sK9:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_46,type,
sK10:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(pred_def_1,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
cl_Groups_Ominus:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
group_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
finite_finite1:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
finite_finite:
!>[X0: $tType] : ( fun(X0,bool) > $o ) ).
tff(pred_def_8,type,
list_all:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_9,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_10,type,
i_Z: ( atom * list(int) ) > $o ).
tff(pred_def_11,type,
pp: bool > $o ).
tff(f2,axiom,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,bool)] :
( finite_finite(X1,X3)
=> finite_finite(X0,image(X1,X0,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_finite__imageI) ).
tff(f3,axiom,
! [X0: $tType,X1: list(X0)] : finite_finite(X0,set(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_finite__set) ).
tff(f131,conjecture,
finite_finite(int,image(product_prod(int,list(int)),int,aa(fun(int,fun(list(int),int)),fun(product_prod(int,list(int)),int),product_prod_case(int,list(int),int),combc(int,fun(list(int),int),fun(list(int),int),aa(fun(int,fun(int,int)),fun(int,fun(fun(list(int),int),fun(list(int),int))),aa(fun(fun(int,int),fun(fun(list(int),int),fun(list(int),int))),fun(fun(int,fun(int,int)),fun(int,fun(fun(list(int),int),fun(list(int),int)))),combb(fun(int,int),fun(fun(list(int),int),fun(list(int),int)),int),combb(int,int,list(int))),minus_minus(int)),combc(list(int),list(int),int,iprod(int),xs))),set(product_prod(int,list(int)),lbounds(as)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f132,negated_conjecture,
~ finite_finite(int,image(product_prod(int,list(int)),int,aa(fun(int,fun(list(int),int)),fun(product_prod(int,list(int)),int),product_prod_case(int,list(int),int),combc(int,fun(list(int),int),fun(list(int),int),aa(fun(int,fun(int,int)),fun(int,fun(fun(list(int),int),fun(list(int),int))),aa(fun(fun(int,int),fun(fun(list(int),int),fun(list(int),int))),fun(fun(int,fun(int,int)),fun(int,fun(fun(list(int),int),fun(list(int),int)))),combb(fun(int,int),fun(fun(list(int),int),fun(list(int),int)),int),combb(int,int,list(int))),minus_minus(int)),combc(list(int),list(int),int,iprod(int),xs))),set(product_prod(int,list(int)),lbounds(as)))),
inference(negated_conjecture,[status(cth)],[f131]) ).
tff(f133,plain,
~ finite_finite(int,image(product_prod(int,list(int)),int,aa(fun(int,fun(list(int),int)),fun(product_prod(int,list(int)),int),product_prod_case(int,list(int),int),combc(int,fun(list(int),int),fun(list(int),int),aa(fun(int,fun(int,int)),fun(int,fun(fun(list(int),int),fun(list(int),int))),aa(fun(fun(int,int),fun(fun(list(int),int),fun(list(int),int))),fun(fun(int,fun(int,int)),fun(int,fun(fun(list(int),int),fun(list(int),int)))),combb(fun(int,int),fun(fun(list(int),int),fun(list(int),int)),int),combb(int,int,list(int))),minus_minus(int)),combc(list(int),list(int),int,iprod(int),xs))),set(product_prod(int,list(int)),lbounds(as)))),
inference(flattening,[],[f132]) ).
tff(f150,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,bool)] :
( finite_finite(X0,image(X1,X0,X2,X3))
| ~ finite_finite(X1,X3) ),
inference(ennf_transformation,[],[f2]) ).
tff(f192,plain,
~ finite_finite(int,image(product_prod(int,list(int)),int,aa(fun(int,fun(list(int),int)),fun(product_prod(int,list(int)),int),product_prod_case(int,list(int),int),combc(int,fun(list(int),int),fun(list(int),int),aa(fun(int,fun(int,int)),fun(int,fun(fun(list(int),int),fun(list(int),int))),aa(fun(fun(int,int),fun(fun(list(int),int),fun(list(int),int))),fun(fun(int,fun(int,int)),fun(int,fun(fun(list(int),int),fun(list(int),int)))),combb(fun(int,int),fun(fun(list(int),int),fun(list(int),int)),int),combb(int,int,list(int))),minus_minus(int)),combc(list(int),list(int),int,iprod(int),xs))),set(product_prod(int,list(int)),lbounds(as)))),
inference(cnf_transformation,[],[f133]) ).
tff(f217,plain,
! [X0: $tType,X1: list(X0)] : finite_finite(X0,set(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
tff(f218,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,bool)] :
( finite_finite(X0,image(X1,X0,X2,X3))
| ~ finite_finite(X1,X3) ),
inference(cnf_transformation,[],[f150]) ).
tff(f281,plain,
~ finite_finite(product_prod(int,list(int)),set(product_prod(int,list(int)),lbounds(as))),
inference(resolution,[],[f192,f218]) ).
tff(f283,plain,
$false,
inference(forward_subsumption_resolution,[],[f281,f217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COM088_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n006.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Mon Sep 28 21:53:10 UTC 2026
% 0.22/0.28 % CPUTime :
% 0.22/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.31 Running first-order theorem proving
% 0.22/0.31 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.09/1.63 % (246170)Detected formulas, will run a generic FOF schedule.
% 4.09/1.63 % (246184)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4271677786:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.09/1.63 % (246184)First to succeed.
% 4.09/1.63 % (246184)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-246170"
% 4.09/1.63 % (246181)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=3814256750:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.09/1.63 % (246181)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.09/1.63 % (246185)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2415330102:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.09/1.63 % (246183)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4061046962:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.09/1.63 % (246179)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=1480399322:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.09/1.63 % (246180)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=1135397004:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.09/1.63 % (246183)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.09/1.63 % (246183)Also succeeded, but the first one will report.
% 4.09/1.63 % (246185)Also succeeded, but the first one will report.
% 4.09/1.63 % (246186)dis-21_1_sil=8000:lcm=predicate:random_seed=3190975404: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)
% 4.09/1.63 % (246186)Also succeeded, but the first one will report.
% 4.09/1.63 % (246184)Refutation found. Thanks to Tanya!
% 4.09/1.63 % SZS status Theorem for theBenchmark
% 4.09/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 4.09/1.63 % (246184)------------------------------
% 4.09/1.63 % (246184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.63 % (246184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.63 % (246184)CaDiCaL version: 2.1.3
% 4.09/1.63 % (246184)Termination reason: Refutation
% 4.09/1.63 % (246184)Time elapsed: 0.004 s
% 4.09/1.63 % (246184)Peak memory usage: 88 MB
% 4.09/1.63 % (246184)Instructions burned: 9 (million)
% 4.09/1.63 % (246184)------------------------------
% 4.09/1.63 % (246184)------------------------------
% 4.09/1.63 % (246170)Success in time 0.448 s
% 4.09/1.63 % Vampire exiting
%------------------------------------------------------------------------------