%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL829_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 : 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 12:00:46 PM UTC 2026
% Result : Theorem 0.18s 0.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 3 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 7 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 65 ( 65 usr; 14 con; 0-6 aty)
% Number of variables : 14 ( 12 !; 2 ?; 14 :)
% 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,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,fun(X1,X2)) > fun(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] : fun(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,
n_lists:
!>[X0: $tType] : ( ( nat * list(X0) ) > list(list(X0)) ) ).
tff(func_def_6,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_7,type,
it: fun(dB,bool) ).
tff(func_def_8,type,
var: nat > dB ).
tff(func_def_9,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_10,type,
dB_rec:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,fun(X0,fun(X0,X0)))) * fun(dB,fun(X0,X0)) * dB ) > X0 ) ).
tff(func_def_11,type,
dB_size: dB > nat ).
tff(func_def_12,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_13,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_14,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_15,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_16,type,
concat:
!>[X0: $tType] : ( list(list(X0)) > list(X0) ) ).
tff(func_def_17,type,
filter:
!>[X0: $tType] : ( fun(X0,bool) > fun(list(X0),list(X0)) ) ).
tff(func_def_18,type,
hd:
!>[X0: $tType] : fun(list(X0),X0) ).
tff(func_def_19,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_20,type,
cons:
!>[X0: $tType] : fun(X0,fun(list(X0),list(X0))) ).
tff(func_def_21,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_22,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) ) > fun(list(X1),X0) ) ).
tff(func_def_23,type,
list_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).
tff(func_def_24,type,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
tff(func_def_25,type,
map:
!>[X0: $tType,X1: $tType] : fun(fun(X0,X1),fun(list(X0),list(X1))) ).
tff(func_def_26,type,
maps:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,list(X1)) * list(X0) ) > list(X1) ) ).
tff(func_def_27,type,
monoid_add_listsum:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_28,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_29,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_30,type,
tl:
!>[X0: $tType] : fun(list(X0),list(X0)) ).
tff(func_def_31,type,
transpose:
!>[X0: $tType] : ( list(list(X0)) > list(list(X0)) ) ).
tff(func_def_32,type,
transpose_rel:
!>[X0: $tType] : fun(list(list(X0)),fun(list(list(X0)),bool)) ).
tff(func_def_33,type,
suc: nat > nat ).
tff(func_def_34,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_35,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_36,type,
fFalse: bool ).
tff(func_def_37,type,
fNot: fun(bool,bool) ).
tff(func_def_38,type,
fTrue: bool ).
tff(func_def_39,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_40,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_41,type,
a: dB ).
tff(func_def_42,type,
as: list(dB) ).
tff(func_def_43,type,
i: nat ).
tff(func_def_44,type,
n: nat ).
tff(func_def_45,type,
t: dB ).
tff(func_def_46,type,
u: dB ).
tff(func_def_47,type,
ua: dB ).
tff(func_def_48,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > X1 ) ).
tff(func_def_49,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > list(X1) ) ).
tff(func_def_50,type,
sK2:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > X0 ) ).
tff(func_def_51,type,
sK3:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > list(X0) ) ).
tff(func_def_52,type,
sK4:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > X1 ) ).
tff(func_def_53,type,
sK5:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > list(X1) ) ).
tff(func_def_54,type,
sK6:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > X0 ) ).
tff(func_def_55,type,
sK7:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > list(X0) ) ).
tff(func_def_56,type,
sK8:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).
tff(func_def_57,type,
sK9:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > list(X0) ) ).
tff(func_def_58,type,
sK10:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_59,type,
sK11:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_60,type,
sK12:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_61,type,
sK13:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_62,type,
sK14:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
equal_equal:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_4,type,
listMem:
!>[X0: $tType] : ( ( X0 * list(X0) ) > $o ) ).
tff(pred_def_5,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_6,type,
member1:
!>[X0: $tType] : ( ( list(X0) * X0 ) > $o ) ).
tff(pred_def_7,type,
null:
!>[X0: $tType] : ( list(X0) > $o ) ).
tff(pred_def_8,type,
accp:
!>[X0: $tType] : ( ( fun(X0,fun(X0,bool)) * X0 ) > $o ) ).
tff(pred_def_9,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_10,type,
pp: bool > $o ).
tff(f5,axiom,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096IT_A_Ia_091u_Pi_093_J_096) ).
tff(f6,axiom,
listsp(dB,it,aa(list(dB),list(dB),aa(fun(dB,dB),fun(list(dB),list(dB)),map(dB,dB),aa(nat,fun(dB,dB),combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),combc(dB,dB,fun(nat,dB),subst),u)),i)),as)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Cons_I3_J) ).
tff(f56,axiom,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( listsp(X0,X2,X1)
<=> ( ( X1 = nil(X0) )
| ? [X3: X0,X4: list(X0)] :
( ( X1 = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) )
& pp(aa(X0,bool,X2,X3))
& listsp(X0,X2,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_listsp_Osimps) ).
tff(f116,conjecture,
listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),aa(list(dB),list(dB),aa(fun(dB,dB),fun(list(dB),list(dB)),map(dB,dB),aa(nat,fun(dB,dB),combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),combc(dB,dB,fun(nat,dB),subst),u)),i)),as))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f117,negated_conjecture,
~ listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),aa(list(dB),list(dB),aa(fun(dB,dB),fun(list(dB),list(dB)),map(dB,dB),aa(nat,fun(dB,dB),combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),combc(dB,dB,fun(nat,dB),subst),u)),i)),as))),
inference(negated_conjecture,[status(cth)],[f116]) ).
tff(f118,plain,
~ listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),aa(list(dB),list(dB),aa(fun(dB,dB),fun(list(dB),list(dB)),map(dB,dB),aa(nat,fun(dB,dB),combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),combc(dB,dB,fun(nat,dB),subst),u)),i)),as))),
inference(flattening,[],[f117]) ).
tff(f142,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
inference(cnf_transformation,[],[f5]) ).
tff(f143,plain,
listsp(dB,it,aa(list(dB),list(dB),aa(fun(dB,dB),fun(list(dB),list(dB)),map(dB,dB),aa(nat,fun(dB,dB),combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),combc(dB,dB,fun(nat,dB),subst),u)),i)),as)),
inference(cnf_transformation,[],[f6]) ).
tff(f213,plain,
! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: list(X0),X4: list(X0)] :
( ~ listsp(X0,X2,X4)
| ~ pp(aa(X0,bool,X2,X3))
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 )
| listsp(X0,X2,X1) ),
inference(cnf_transformation,[],[f56]) ).
tff(f282,plain,
~ listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),aa(list(dB),list(dB),aa(fun(dB,dB),fun(list(dB),list(dB)),map(dB,dB),aa(nat,fun(dB,dB),combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),combc(dB,dB,fun(nat,dB),subst),u)),i)),as))),
inference(cnf_transformation,[],[f118]) ).
tff(f301,plain,
! [X0: $tType,X2: fun(X0,bool),X3: X0,X4: list(X0)] :
( listsp(X0,X2,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4))
| ~ pp(aa(X0,bool,X2,X3))
| ~ listsp(X0,X2,X4) ),
inference(equality_resolution,[],[f213]) ).
tff(f583,plain,
( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))
| ~ listsp(dB,it,aa(list(dB),list(dB),aa(fun(dB,dB),fun(list(dB),list(dB)),map(dB,dB),aa(nat,fun(dB,dB),combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),combc(dB,dB,fun(nat,dB),subst),u)),i)),as)) ),
inference(resolution,[],[f301,f282]) ).
tff(f593,plain,
~ listsp(dB,it,aa(list(dB),list(dB),aa(fun(dB,dB),fun(list(dB),list(dB)),map(dB,dB),aa(nat,fun(dB,dB),combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),combc(dB,dB,fun(nat,dB),subst),u)),i)),as)),
inference(forward_subsumption_resolution,[],[f583,f142]) ).
tff(f594,plain,
$false,
inference(forward_subsumption_resolution,[],[f593,f143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL829_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 16:58:16 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.18/0.50 % (1011587)Will run a generic schedule for satisfiability detection.
% 0.18/0.50 % (1011593)% WARNING: option uhcvi not known.
% 0.18/0.50 % (1011593)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=77434708:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.50 % (1011592)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2983256327_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.50 % (1011594)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3675197576:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.50 % (1011595)dis+10_1_sil=32000:sp=arity:random_seed=2157424065:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.50 % (1011596)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=301741395:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.50 % Exception at run slice level
% 0.18/0.50 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.50 % (1011597)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2412439949:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.50 % (1011598)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=16737015:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.50 % (1011604)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1742723857:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.50 % Exception at run slice level
% 0.18/0.50 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.50 % (1011596) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1011587-1011596"...
% 0.18/0.50 % (1011596)...printing done.
% 0.18/0.50 % (1011596)Refutation found. Thanks to Tanya!
% 0.18/0.50 % SZS status Theorem for theBenchmark
% 0.18/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50 % (1011596)------------------------------
% 0.18/0.50 % (1011596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.50 % (1011596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.50 % (1011596)CaDiCaL version: 2.1.3
% 0.18/0.50 % (1011596)Termination reason: Refutation
% 0.18/0.50 % (1011596)Time elapsed: 0.037 s
% 0.18/0.50 % (1011596)Peak memory usage: 12 MB
% 0.18/0.50 % (1011596)Instructions burned: 58 (million)
% 0.18/0.50 % (1011587)Success in time 0.086 s
% 0.18/0.51 % Vampire exiting
%------------------------------------------------------------------------------