%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL838_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 : n010.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 12:00:48 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 4 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 62 ( 62 usr; 21 con; 0-5 aty)
% Number of variables : 33 ( 31 !; 2 ?; 33 :)
% 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,
type: $tType ).
tff(type_def_10,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,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
it: fun(dB,bool) ).
tff(func_def_6,type,
abs: dB > dB ).
tff(func_def_7,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_8,type,
var: nat > dB ).
tff(func_def_9,type,
dB_size: dB > nat ).
tff(func_def_10,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_11,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_12,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_13,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_14,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_15,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_16,type,
suc: nat > nat ).
tff(func_def_17,type,
shift:
!>[X0: $tType] : ( ( fun(nat,X0) * nat * X0 ) > fun(nat,X0) ) ).
tff(func_def_18,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_19,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_20,type,
fFalse: bool ).
tff(func_def_21,type,
fTrue: bool ).
tff(func_def_22,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_23,type,
t1: type ).
tff(func_def_24,type,
t_a: type ).
tff(func_def_25,type,
t: type ).
tff(func_def_26,type,
a: dB ).
tff(func_def_27,type,
as: list(dB) ).
tff(func_def_28,type,
e: fun(nat,type) ).
tff(func_def_29,type,
ea: fun(nat,type) ).
tff(func_def_30,type,
i: nat ).
tff(func_def_31,type,
ia: nat ).
tff(func_def_32,type,
r: dB ).
tff(func_def_33,type,
t2: dB ).
tff(func_def_34,type,
u: dB ).
tff(func_def_35,type,
ua: dB ).
tff(func_def_36,type,
sK0: ( dB * fun(nat,type) ) > type ).
tff(func_def_37,type,
sK1: ( dB * fun(nat,type) ) > type ).
tff(func_def_38,type,
sK2: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_39,type,
sK3: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_40,type,
sK4: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_41,type,
sK5: ( dB * dB ) > dB ).
tff(func_def_42,type,
sK6: ( dB * dB * dB ) > dB ).
tff(func_def_43,type,
sK7: ( dB * dB * dB ) > dB ).
tff(func_def_44,type,
sK8: ( dB * dB * dB ) > dB ).
tff(func_def_45,type,
sK9: nat > nat ).
tff(func_def_46,type,
sK10: fun(nat,bool) > nat ).
tff(func_def_47,type,
sK11: fun(nat,bool) > nat ).
tff(func_def_48,type,
sK12: nat > nat ).
tff(func_def_49,type,
sK13:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_50,type,
sK14: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_51,type,
sK15: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_52,type,
sK16: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).
tff(func_def_53,type,
sK17: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).
tff(func_def_54,type,
sK18: dB > dB ).
tff(func_def_55,type,
sK19: dB > dB ).
tff(func_def_56,type,
sK20: dB > list(dB) ).
tff(func_def_57,type,
sK21: dB > dB ).
tff(func_def_58,type,
sK22: dB > list(dB) ).
tff(func_def_59,type,
sK23: dB > nat ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
beta: ( dB * dB ) > $o ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
typing: ( fun(nat,type) * dB * type ) > $o ).
tff(pred_def_5,type,
typings: ( fun(nat,type) * list(dB) * list(type) ) > $o ).
tff(pred_def_6,type,
pp: bool > $o ).
tff(f4,axiom,
typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_T) ).
tff(f75,axiom,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( typing(X3,foldl(dB,dB,app,X2,X1),X0)
=> ? [X4: list(type)] :
( typing(X3,X2,foldr(type,type,fun1,X4,X0))
& typings(X3,X1,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_list__app__typeD) ).
tff(f103,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/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f109,axiom,
! [X0: type] :
( typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0)
=> thesis ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f110,conjecture,
thesis,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f111,negated_conjecture,
~ thesis,
inference(negated_conjecture,[status(cth)],[f110]) ).
tff(f114,plain,
~ thesis,
inference(flattening,[],[f111]) ).
tff(f163,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( typing(X3,X2,foldr(type,type,fun1,X4,X0))
& typings(X3,X1,X4) )
| ~ typing(X3,foldl(dB,dB,app,X2,X1),X0) ),
inference(ennf_transformation,[],[f75]) ).
tff(f175,plain,
! [X0: type] :
( thesis
| ~ typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0) ),
inference(ennf_transformation,[],[f109]) ).
tff(f179,plain,
typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t1),
inference(cnf_transformation,[],[f4]) ).
tff(f273,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( typing(X3,X2,foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0))
| ~ typing(X3,foldl(dB,dB,app,X2,X1),X0) ),
inference(cnf_transformation,[],[f163]) ).
tff(f321,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,[],[f103]) ).
tff(f327,plain,
! [X0: type] :
( ~ typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0)
| thesis ),
inference(cnf_transformation,[],[f175]) ).
tff(f328,plain,
~ thesis,
inference(cnf_transformation,[],[f114]) ).
tff(f347,plain,
! [X0: type] : ~ typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0),
inference(forward_subsumption_resolution,[],[f327,f328]) ).
tff(f407,plain,
typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as),t1),
inference(forward_demodulation,[],[f179,f321]) ).
tff(f408,plain,
! [X0: type] : ~ typing(shift(type,e,i,t),aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),X0),
inference(forward_demodulation,[],[f347,f321]) ).
tff(f608,plain,
! [X0: list(dB),X1: type] : ~ typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),X0),X1),
inference(resolution,[],[f273,f408]) ).
tff(f685,plain,
$false,
inference(resolution,[],[f407,f608]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL838_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n010.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 16:59:16 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.16/0.48 % (1166547)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (1166556)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=328137718:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (1166553)% WARNING: option uhcvi not known.
% 0.16/0.48 % (1166552)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2714976551_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (1166555)dis+10_1_sil=32000:sp=arity:random_seed=738963233:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (1166553)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=427310994:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (1166554)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2955265580:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (1166557)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=930705988:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (1166558)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2279701030:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % Exception at run slice level
% 0.16/0.48 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.48 % (1166556) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1166547-1166556"...
% 0.16/0.48 % (1166556)...printing done.
% 0.16/0.48 % (1166556)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (1166556)------------------------------
% 0.16/0.48 % (1166556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (1166556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (1166556)CaDiCaL version: 2.1.3
% 0.16/0.48 % (1166556)Termination reason: Refutation
% 0.16/0.48 % (1166556)Time elapsed: 0.018 s
% 0.16/0.48 % (1166556)Peak memory usage: 12 MB
% 0.16/0.48 % (1166556)Instructions burned: 54 (million)
% 0.16/0.48 % (1166547)Success in time 0.064 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------