%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL839_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 : n016.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 12:00:49 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 9 |; 2 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 4 prp; 0-3 aty)
% Number of functors : 62 ( 62 usr; 23 con; 0-5 aty)
% Number of variables : 23 ( 0 sgn 22 !; 1 ?; 23 :)
% 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,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_10,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_11,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_12,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_13,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_14,type,
suc: nat > nat ).
tff(func_def_15,type,
shift:
!>[X0: $tType] : ( ( fun(nat,X0) * nat * X0 ) > fun(nat,X0) ) ).
tff(func_def_16,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_17,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_18,type,
fFalse: bool ).
tff(func_def_19,type,
fTrue: bool ).
tff(func_def_20,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_21,type,
t1: type ).
tff(func_def_22,type,
t_a: type ).
tff(func_def_23,type,
t: type ).
tff(func_def_24,type,
ua1: type ).
tff(func_def_25,type,
a: dB ).
tff(func_def_26,type,
as: list(dB) ).
tff(func_def_27,type,
e: fun(nat,type) ).
tff(func_def_28,type,
ea: fun(nat,type) ).
tff(func_def_29,type,
i: nat ).
tff(func_def_30,type,
ia: nat ).
tff(func_def_31,type,
r: dB ).
tff(func_def_32,type,
t2: dB ).
tff(func_def_33,type,
u: dB ).
tff(func_def_34,type,
ua: dB ).
tff(func_def_35,type,
sK1: type ).
tff(func_def_36,type,
sK2: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_37,type,
sK3: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_38,type,
sK4: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_39,type,
sK5: ( dB * dB ) > dB ).
tff(func_def_40,type,
sK6: ( dB * fun(nat,type) ) > type ).
tff(func_def_41,type,
sK7: ( dB * fun(nat,type) ) > type ).
tff(func_def_42,type,
sK8: ( dB * dB * dB ) > dB ).
tff(func_def_43,type,
sK9: ( dB * dB * dB ) > dB ).
tff(func_def_44,type,
sK10: ( dB * dB * dB ) > dB ).
tff(func_def_45,type,
sK11: nat > nat ).
tff(func_def_46,type,
sK12: fun(nat,bool) > nat ).
tff(func_def_47,type,
sK13: fun(nat,bool) > nat ).
tff(func_def_48,type,
sK14: nat > nat ).
tff(func_def_49,type,
sK15:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_50,type,
sK16: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).
tff(func_def_51,type,
sK17: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).
tff(func_def_52,type,
sK18: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_53,type,
sK19: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_54,type,
sK20: dB > dB ).
tff(func_def_55,type,
sK21: dB > dB ).
tff(func_def_56,type,
sK22: dB > list(dB) ).
tff(func_def_57,type,
sK23: dB > list(dB) ).
tff(func_def_58,type,
sK24: dB > nat ).
tff(func_def_59,type,
sK25: dB > dB ).
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(pred_def_8,type,
sP0: dB > $o ).
tff(f4,axiom,
typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),ua1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096e_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_096) ).
tff(f27,axiom,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0)
=> ~ ! [X4: type] :
( typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,X4),X0))
=> ~ typing(X3,X1,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_typing__elims_I2_J) ).
tff(f109,axiom,
! [X0: type] :
( typing(shift(type,e,i,t),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(f135,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( typing(X3,X1,X4)
& typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,X4),X0)) )
| ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(ennf_transformation,[],[f27]) ).
tff(f176,plain,
! [X0: type] :
( thesis
| ~ typing(shift(type,e,i,t),a,X0) ),
inference(ennf_transformation,[],[f109]) ).
tff(f183,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ( typing(X3,X1,sK4(X0,X1,X2,X3))
& typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,sK4(X0,X1,X2,X3)),X0)) )
| ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X4,sK4(X0,X1,X2,X3))],[f135]) ).
tff(f220,plain,
typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),ua1),
inference(cnf_transformation,[],[f4]) ).
tff(f247,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0)
| typing(X3,X1,sK4(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f183]) ).
tff(f366,plain,
! [X0: type] :
( thesis
| ~ typing(shift(type,e,i,t),a,X0) ),
inference(cnf_transformation,[],[f176]) ).
tff(f367,plain,
~ thesis,
inference(cnf_transformation,[],[f114]) ).
tff(f389,definition,
( spl26_1
<=> ! [X0: type] : ~ typing(shift(type,e,i,t),a,X0) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
tff(f390,plain,
( ! [X0: type] : ~ typing(shift(type,e,i,t),a,X0)
| ~ spl26_1 ),
inference(avatar_component_clause,[],[f389]) ).
tff(f392,definition,
( spl26_2
<=> thesis ),
introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition]) ).
tff(f395,plain,
( spl26_1
| spl26_2 ),
inference(avatar_split_clause,[],[f366,f392,f389]) ).
tff(f396,plain,
~ spl26_2,
inference(avatar_split_clause,[],[f367,f392]) ).
tff(f574,plain,
typing(shift(type,e,i,t),a,sK4(ua1,a,abs(r),shift(type,e,i,t))),
inference(resolution,[],[f247,f220]) ).
tff(f579,plain,
( $false
| ~ spl26_1 ),
inference(forward_subsumption_resolution,[],[f574,f390]) ).
tff(f580,plain,
~ spl26_1,
inference(avatar_contradiction_clause,[],[f579]) ).
cnf(s1,plain,
( spl26_1
| spl26_2 ),
inference(sat_conversion,[],[f395]) ).
cnf(s2,plain,
~ spl26_2,
inference(sat_conversion,[],[f396]) ).
cnf(s8,plain,
~ spl26_1,
inference(sat_conversion,[],[f580]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s2,s8]) ).
tff(f581,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL839_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n016.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 17:04:02 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.17/0.47 % (2849155)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (2849163)dis+10_1_sil=32000:sp=arity:random_seed=2046790579:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (2849161)% WARNING: option uhcvi not known.
% 0.17/0.47 % (2849162)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=520902682:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (2849160)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3108943805_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (2849161)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3965154805:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (2849164)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=444670207:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (2849165)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1599744627:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (2849166)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1898280341:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (2849163) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2849155-2849163"...
% 0.17/0.47 % (2849163)...printing done.
% 0.17/0.47 % (2849163)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (2849163)------------------------------
% 0.17/0.47 % (2849163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (2849163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (2849163)CaDiCaL version: 2.1.3
% 0.17/0.47 % (2849163)Termination reason: Refutation
% 0.17/0.47 % (2849163)Time elapsed: 0.010 s
% 0.17/0.47 % (2849163)Peak memory usage: 12 MB
% 0.17/0.47 % (2849163)Instructions burned: 25 (million)
% 0.17/0.47 % (2849155)Success in time 0.041 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------