%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM088_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 : n001.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 09:40:17 AM UTC 2026
% Result : Theorem 0.12s 0.26s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 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 : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 54 ( 54 usr; 8 con; 0-5 aty)
% Number of variables : 22 ( 22 !; 0 ?; 22 :)
% 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,X1: $tType] : ( ( fun(X1,bool) * fun(X1,X0) * X0 ) > X1 ) ).
tff(func_def_38,type,
sK2:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,bool) * fun(X1,X0) * X0 ) > X1 ) ).
tff(func_def_39,type,
sK3:
!>[X0: $tType] : ( fun(X0,bool) > list(X0) ) ).
tff(func_def_40,type,
sK4:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) * fun(X1,bool) ) > X1 ) ).
tff(func_def_41,type,
sK5:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).
tff(func_def_42,type,
sK6:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) * X0 ) > X0 ) ).
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(func_def_47,type,
sK11:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).
tff(func_def_48,type,
sK12:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) * list(X0) ) > X0 ) ).
tff(func_def_49,type,
sK13:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_50,type,
sK14:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
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/sandbox/benchmark/theBenchmark.p',fact_1_finite__imageI) ).
tff(f3,axiom,
! [X0: $tType,X1: list(X0)] : finite_finite(X0,set(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_finite__set) ).
tff(f23,axiom,
! [X0: $tType,X1: $tType,X2: $tType] : ( produc1605651328_split(X2,X1,X0) = product_prod_case(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_internal__split__def) ).
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/sandbox/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(f137,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(f221,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,[],[f137]) ).
tff(f222,plain,
! [X0: $tType,X1: list(X0)] : finite_finite(X0,set(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
tff(f250,plain,
! [X1: $tType,X0: $tType,X2: $tType] : ( product_prod_case(X2,X1,X0) = produc1605651328_split(X2,X1,X0) ),
inference(cnf_transformation,[],[f23]) ).
tff(f386,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(f389,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),produc1605651328_split(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(definition_unfolding,[],[f386,f250]) ).
tff(f576,plain,
~ finite_finite(product_prod(int,list(int)),set(product_prod(int,list(int)),lbounds(as))),
inference(resolution,[],[f389,f221]) ).
tff(f577,plain,
$false,
inference(forward_subsumption_resolution,[],[f576,f222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM088_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.16 % Computer : n001.cluster.edu
% 0.12/0.16 % Model : x86_64 x86_64
% 0.12/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.16 % Memory : 8046.5625MB
% 0.12/0.16 % OS : Linux 6.8.0-71-generic
% 0.12/0.16 % CPULimit : 300
% 0.12/0.16 % WCLimit : 300
% 0.12/0.16 % DateTime : Mon Sep 28 21:59:19 UTC 2026
% 0.12/0.16 % CPUTime :
% 0.12/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.20 Running first-order model finding
% 0.12/0.20 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
% 0.12/0.26 % (789929)Will run a generic schedule for satisfiability detection.
% 0.12/0.26 % (789953)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2766366172:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.26 % (789949)% WARNING: option uhcvi not known.
% 0.12/0.26 % (789948)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3942071281_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.26 % (789951)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4067593202:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.26 % (789952)dis+10_1_sil=32000:sp=arity:random_seed=3305929769:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.26 % (789954)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2334660290:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.26 % (789955)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2460949993:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.26 % (789953) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-789929-789953"...
% 0.12/0.26 % (789953)...printing done.
% 0.12/0.26 % (789953)Refutation found. Thanks to Tanya!
% 0.12/0.26 % SZS status Theorem for theBenchmark
% 0.12/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.26 % (789953)------------------------------
% 0.12/0.26 % (789953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.26 % (789953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.26 % (789953)CaDiCaL version: 2.1.3
% 0.12/0.26 % (789953)Termination reason: Refutation
% 0.12/0.26 % (789953)Time elapsed: 0.009 s
% 0.12/0.26 % (789953)Peak memory usage: 12 MB
% 0.12/0.26 % (789953)Instructions burned: 28 (million)
% 0.12/0.26 % (789929)Success in time 0.051 s
% 0.12/0.26 % Vampire exiting
%------------------------------------------------------------------------------