%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL953_8 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 12:01:15 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 65 ( 15 unt; 0 typ; 4 def)
% Number of atoms : 386 ( 0 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 375 ( 150 ~; 140 |; 36 &)
% ( 4 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 96 ( 96 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 7 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 142 ( 0 sgn 118 !; 24 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_2,type,
sK0: '$ki_world' > $i ).
tff(func_def_3,type,
sK1: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_4,type,
sK2: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_5,type,
sK3: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_8,type,
sK6: '$ki_world' > '$ki_world' ).
tff(func_def_9,type,
sK7: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_10,type,
sK8: '$ki_world' ).
tff(func_def_12,type,
sK10: '$ki_world' ).
tff(func_def_14,type,
sK12: '$ki_world' ).
tff(func_def_15,type,
sK13: '$ki_world' ).
tff(func_def_16,type,
sK14: '$ki_world' > '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
in: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_3,type,
disjoint: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_4,type,
empty: ( '$ki_world' * $i ) > $o ).
tff(pred_def_5,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f7,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ! [X3: $i] :
( '$ki_exists_in_world_$i'(X2,X3)
=> ! [X4: '$ki_world'] :
( '$ki_accessible'(X2,X4)
=> ( ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> ~ ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> in(X6,X1,X3) ) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> disjoint(X5,singleton(X1),X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
tff(f8,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ! [X3: $i] :
( '$ki_exists_in_world_$i'(X2,X3)
=> ! [X4: '$ki_world'] :
( '$ki_accessible'(X2,X4)
=> ( ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> ~ ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> in(X6,X1,X3) ) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> disjoint(X5,singleton(X1),X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f9,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ! [X3: $i] :
( '$ki_exists_in_world_$i'(X2,X3)
=> ! [X4: '$ki_world'] :
( '$ki_accessible'(X2,X4)
=> ( ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> ~ ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> in(X6,X1,X3) ) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> disjoint(X5,singleton(X1),X3) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
tff(f12,plain,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ! [X3: $i] :
( '$ki_exists_in_world_$i'(X2,X3)
=> ! [X4: '$ki_world'] :
( '$ki_accessible'(X2,X4)
=> ( ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> ~ ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> in(X6,X1,X3) ) )
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X4,X7)
=> disjoint(X7,singleton(X1),X3) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
tff(f13,plain,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ! [X3: $i] :
( '$ki_exists_in_world_$i'(X2,X3)
=> ! [X4: '$ki_world'] :
( '$ki_accessible'(X2,X4)
=> ( ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> ~ ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> in(X6,X1,X3) ) )
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X4,X7)
=> disjoint(X7,singleton(X1),X3) ) ) ) ) ) ) ),
inference(rectify,[],[f9]) ).
tff(f20,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ! [X4: '$ki_world'] :
( ! [X7: '$ki_world'] :
( disjoint(X7,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X7) )
| ? [X5: '$ki_world'] :
( ! [X6: '$ki_world'] :
( in(X6,X1,X3)
| ~ '$ki_accessible'(X5,X6) )
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X2,X4) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f12]) ).
tff(f21,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ! [X4: '$ki_world'] :
( ! [X7: '$ki_world'] :
( disjoint(X7,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X7) )
| ? [X5: '$ki_world'] :
( ! [X6: '$ki_world'] :
( in(X6,X1,X3)
| ~ '$ki_accessible'(X5,X6) )
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X2,X4) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f20]) ).
tff(f22,plain,
? [X0: '$ki_world'] :
( ? [X1: $i] :
( ? [X2: '$ki_world'] :
( ? [X3: $i] :
( ? [X4: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(X1),X3)
& '$ki_accessible'(X4,X7) )
& ! [X5: '$ki_world'] :
( ? [X6: '$ki_world'] :
( ~ in(X6,X1,X3)
& '$ki_accessible'(X5,X6) )
| ~ '$ki_accessible'(X4,X5) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f13]) ).
tff(f23,plain,
? [X0: '$ki_world'] :
( ? [X1: $i] :
( ? [X2: '$ki_world'] :
( ? [X3: $i] :
( ? [X4: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(X1),X3)
& '$ki_accessible'(X4,X7) )
& ! [X5: '$ki_world'] :
( ? [X6: '$ki_world'] :
( ~ in(X6,X1,X3)
& '$ki_accessible'(X5,X6) )
| ~ '$ki_accessible'(X4,X5) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f22]) ).
tff(f31,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X5) )
| ? [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( in(X7,X1,X3)
| ~ '$ki_accessible'(X6,X7) )
& '$ki_accessible'(X4,X6) )
| ~ '$ki_accessible'(X2,X4) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(rectify,[],[f21]) ).
tff(f32,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X5) )
| ( ! [X7: '$ki_world'] :
( in(X7,X1,X3)
| ~ '$ki_accessible'(sK7(X1,X3,X4),X7) )
& '$ki_accessible'(X4,sK7(X1,X3,X4)) )
| ~ '$ki_accessible'(X2,X4) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X6,sK7(X1,X3,X4))],[f31]) ).
tff(f33,plain,
? [X0: '$ki_world'] :
( ? [X1: $i] :
( ? [X2: '$ki_world'] :
( ? [X3: $i] :
( ? [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ disjoint(X5,singleton(X1),X3)
& '$ki_accessible'(X4,X5) )
& ! [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ in(X7,X1,X3)
& '$ki_accessible'(X6,X7) )
| ~ '$ki_accessible'(X4,X6) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(rectify,[],[f23]) ).
tff(f34,plain,
( ~ disjoint(sK13,singleton(sK9),sK11)
& '$ki_accessible'(sK12,sK13)
& ! [X6: '$ki_world'] :
( ( ~ in(sK14(X6),sK9,sK11)
& '$ki_accessible'(X6,sK14(X6)) )
| ~ '$ki_accessible'(sK12,X6) )
& '$ki_accessible'(sK10,sK12)
& '$ki_exists_in_world_$i'(sK10,sK11)
& '$ki_accessible'(sK8,sK10)
& '$ki_exists_in_world_$i'(sK8,sK9)
& '$ki_accessible'('$ki_local_world',sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12,sK13,sK14]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11),skolemize(X4,sK12),skolemize(X5,sK13),skolemize(X7,sK14(X6))],[f33]) ).
tff(f48,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ '$ki_accessible'(X4,X5)
| '$ki_accessible'(X4,sK7(X1,X3,X4))
| ~ '$ki_accessible'(X2,X4)
| disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f32]) ).
tff(f49,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X7: '$ki_world',X4: '$ki_world',X5: '$ki_world'] :
( ~ '$ki_accessible'(sK7(X1,X3,X4),X7)
| ~ '$ki_accessible'(X4,X5)
| in(X7,X1,X3)
| disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X2,X4)
| ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f32]) ).
tff(f50,plain,
'$ki_accessible'('$ki_local_world',sK8),
inference(cnf_transformation,[],[f34]) ).
tff(f51,plain,
'$ki_exists_in_world_$i'(sK8,sK9),
inference(cnf_transformation,[],[f34]) ).
tff(f52,plain,
'$ki_accessible'(sK8,sK10),
inference(cnf_transformation,[],[f34]) ).
tff(f53,plain,
'$ki_exists_in_world_$i'(sK10,sK11),
inference(cnf_transformation,[],[f34]) ).
tff(f54,plain,
'$ki_accessible'(sK10,sK12),
inference(cnf_transformation,[],[f34]) ).
tff(f55,plain,
! [X6: '$ki_world'] :
( '$ki_accessible'(X6,sK14(X6))
| ~ '$ki_accessible'(sK12,X6) ),
inference(cnf_transformation,[],[f34]) ).
tff(f56,plain,
! [X6: '$ki_world'] :
( ~ in(sK14(X6),sK9,sK11)
| ~ '$ki_accessible'(sK12,X6) ),
inference(cnf_transformation,[],[f34]) ).
tff(f57,plain,
'$ki_accessible'(sK12,sK13),
inference(cnf_transformation,[],[f34]) ).
tff(f58,plain,
~ disjoint(sK13,singleton(sK9),sK11),
inference(cnf_transformation,[],[f34]) ).
tff(f218,plain,
! [X2: $i,X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X3,X2)
| '$ki_accessible'(X0,sK7(X2,sK11,X0))
| ~ '$ki_accessible'(sK10,X0)
| disjoint(X1,singleton(X2),sK11)
| ~ '$ki_accessible'(X3,sK10)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X3) ),
inference(resolution,[],[f48,f53]) ).
tff(f261,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( '$ki_accessible'(X0,sK7(sK9,sK11,X0))
| ~ '$ki_accessible'(sK10,X0)
| disjoint(X1,singleton(sK9),sK11)
| ~ '$ki_accessible'(sK8,sK10)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',sK8) ),
inference(resolution,[],[f218,f51]) ).
tff(f264,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( '$ki_accessible'(X0,sK7(sK9,sK11,X0))
| ~ '$ki_accessible'(sK10,X0)
| disjoint(X1,singleton(sK9),sK11)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',sK8) ),
inference(forward_subsumption_resolution,[],[f261,f52]) ).
tff(f267,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(sK10,X0)
| '$ki_accessible'(X0,sK7(sK9,sK11,X0))
| disjoint(X1,singleton(sK9),sK11)
| ~ '$ki_accessible'(X0,X1) ),
inference(forward_subsumption_resolution,[],[f264,f50]) ).
tff(f348,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: '$ki_world',X4: '$ki_world',X5: '$ki_world'] :
( ~ '$ki_accessible'(sK12,sK7(X2,X3,X0))
| in(sK14(sK7(X2,X3,X0)),X2,X3)
| disjoint(X1,singleton(X2),X3)
| ~ '$ki_accessible'(X4,X0)
| ~ '$ki_exists_in_world_$i'(X4,X3)
| ~ '$ki_accessible'(X5,X4)
| ~ '$ki_exists_in_world_$i'(X5,X2)
| ~ '$ki_accessible'('$ki_local_world',X5)
| ~ '$ki_accessible'(X0,X1) ),
inference(resolution,[],[f49,f55]) ).
tff(f405,plain,
! [X0: '$ki_world'] :
( '$ki_accessible'(sK12,sK7(sK9,sK11,sK12))
| disjoint(X0,singleton(sK9),sK11)
| ~ '$ki_accessible'(sK12,X0) ),
inference(resolution,[],[f267,f54]) ).
tff(f501,definition,
( spl15_51
<=> ! [X0: '$ki_world'] :
( disjoint(X0,singleton(sK9),sK11)
| ~ '$ki_accessible'(sK12,X0) ) ),
introduced(definition,[new_symbols(definition,[spl15_51])],[avatar_definition]) ).
tff(f502,plain,
( ! [X0: '$ki_world'] :
( disjoint(X0,singleton(sK9),sK11)
| ~ '$ki_accessible'(sK12,X0) )
| ~ spl15_51 ),
inference(avatar_component_clause,[],[f501]) ).
tff(f504,definition,
( spl15_52
<=> '$ki_accessible'(sK12,sK7(sK9,sK11,sK12)) ),
introduced(definition,[new_symbols(definition,[spl15_52])],[avatar_definition]) ).
tff(f506,plain,
( '$ki_accessible'(sK12,sK7(sK9,sK11,sK12))
| ~ spl15_52 ),
inference(avatar_component_clause,[],[f504]) ).
tff(f507,plain,
( spl15_51
| spl15_52 ),
inference(avatar_split_clause,[],[f405,f504,f501]) ).
tff(f508,plain,
( ~ '$ki_accessible'(sK12,sK13)
| ~ spl15_51 ),
inference(resolution,[],[f502,f58]) ).
tff(f510,plain,
( $false
| ~ spl15_51 ),
inference(forward_subsumption_resolution,[],[f508,f57]) ).
tff(f511,plain,
~ spl15_51,
inference(avatar_contradiction_clause,[],[f510]) ).
tff(f637,definition,
( spl15_62
<=> in(sK14(sK7(sK9,sK11,sK12)),sK9,sK11) ),
introduced(definition,[new_symbols(definition,[spl15_62])],[avatar_definition]) ).
tff(f638,plain,
( ~ in(sK14(sK7(sK9,sK11,sK12)),sK9,sK11)
| spl15_62 ),
inference(avatar_component_clause,[],[f637]) ).
tff(f639,plain,
( in(sK14(sK7(sK9,sK11,sK12)),sK9,sK11)
| ~ spl15_62 ),
inference(avatar_component_clause,[],[f637]) ).
tff(f641,plain,
( ~ '$ki_accessible'(sK12,sK7(sK9,sK11,sK12))
| ~ spl15_62 ),
inference(resolution,[],[f639,f56]) ).
tff(f642,plain,
( $false
| ~ spl15_52
| ~ spl15_62 ),
inference(forward_subsumption_resolution,[],[f641,f506]) ).
tff(f643,plain,
( ~ spl15_52
| ~ spl15_62 ),
inference(avatar_contradiction_clause,[],[f642]) ).
tff(f867,plain,
( ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( in(sK14(sK7(sK9,sK11,sK12)),sK9,sK11)
| disjoint(X0,singleton(sK9),sK11)
| ~ '$ki_accessible'(X1,sK12)
| ~ '$ki_exists_in_world_$i'(X1,sK11)
| ~ '$ki_accessible'(X2,X1)
| ~ '$ki_exists_in_world_$i'(X2,sK9)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(sK12,X0) )
| ~ spl15_52 ),
inference(resolution,[],[f348,f506]) ).
tff(f871,plain,
( ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( disjoint(X0,singleton(sK9),sK11)
| ~ '$ki_accessible'(X1,sK12)
| ~ '$ki_exists_in_world_$i'(X1,sK11)
| ~ '$ki_accessible'(X2,X1)
| ~ '$ki_exists_in_world_$i'(X2,sK9)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(sK12,X0) )
| ~ spl15_52
| spl15_62 ),
inference(forward_subsumption_resolution,[],[f867,f638]) ).
tff(f1304,definition,
( spl15_92
<=> ! [X2: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(X1,sK12)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_exists_in_world_$i'(X2,sK9)
| ~ '$ki_accessible'(X2,X1)
| ~ '$ki_exists_in_world_$i'(X1,sK11) ) ),
introduced(definition,[new_symbols(definition,[spl15_92])],[avatar_definition]) ).
tff(f1305,plain,
( ! [X2: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X2,sK9)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(X1,sK12)
| ~ '$ki_accessible'(X2,X1)
| ~ '$ki_exists_in_world_$i'(X1,sK11) )
| ~ spl15_92 ),
inference(avatar_component_clause,[],[f1304]) ).
tff(f1306,plain,
( spl15_92
| spl15_51
| ~ spl15_52
| spl15_62 ),
inference(avatar_split_clause,[],[f871,f637,f504,f501,f1304]) ).
tff(f1313,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',sK8)
| ~ '$ki_accessible'(X0,sK12)
| ~ '$ki_accessible'(sK8,X0)
| ~ '$ki_exists_in_world_$i'(X0,sK11) )
| ~ spl15_92 ),
inference(resolution,[],[f1305,f51]) ).
tff(f1314,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK11)
| ~ '$ki_accessible'(sK8,X0)
| ~ '$ki_accessible'(X0,sK12) )
| ~ spl15_92 ),
inference(forward_subsumption_resolution,[],[f1313,f50]) ).
tff(f1315,plain,
( ~ '$ki_accessible'(sK8,sK10)
| ~ '$ki_accessible'(sK10,sK12)
| ~ spl15_92 ),
inference(resolution,[],[f1314,f53]) ).
tff(f1316,plain,
( ~ '$ki_accessible'(sK10,sK12)
| ~ spl15_92 ),
inference(forward_subsumption_resolution,[],[f1315,f52]) ).
tff(f1317,plain,
( $false
| ~ spl15_92 ),
inference(forward_subsumption_resolution,[],[f1316,f54]) ).
tff(f1318,plain,
~ spl15_92,
inference(avatar_contradiction_clause,[],[f1317]) ).
cnf(s363,plain,
( spl15_51
| spl15_52 ),
inference(sat_conversion,[],[f507]) ).
cnf(s366,plain,
~ spl15_51,
inference(sat_conversion,[],[f511]) ).
cnf(s448,plain,
( ~ spl15_52
| ~ spl15_62 ),
inference(sat_conversion,[],[f643]) ).
cnf(s903,plain,
( spl15_51
| ~ spl15_52
| spl15_62
| spl15_92 ),
inference(sat_conversion,[],[f1306]) ).
cnf(s915,plain,
~ spl15_92,
inference(sat_conversion,[],[f1318]) ).
cnf(s916,plain,
( spl15_51
| ~ spl15_52
| spl15_62 ),
inference(rat,[],[s903,s915]) ).
cnf(s917,plain,
spl15_52,
inference(rat,[],[s363,s366]) ).
cnf(s918,plain,
spl15_62,
inference(rat,[],[s916,s366,s917]) ).
cnf(s921,plain,
$false,
inference(rat,[],[s448,s918,s917]) ).
tff(f1319,plain,
$false,
inference(avatar_sat_refutation,[],[s921]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL953_8 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 17:08:22 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.17/0.46 % (3755648)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (3755655)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2021645483:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.46 % (3755654)% WARNING: option uhcvi not known.
% 0.17/0.46 % (3755653)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3304145397_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.46 % (3755654)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1862216705:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.46 % (3755658)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3379038924:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.46 % (3755656)dis+10_1_sil=32000:sp=arity:random_seed=2075088430:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.46 % (3755657)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1818394319:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.46 % (3755659)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1408926689:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.46 % TRYING [1]
% 0.17/0.46 % TRYING [2]
% 0.17/0.46 % (3755659) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3755648-3755659"...
% 0.17/0.46 % (3755655) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3755648-3755655"...
% 0.17/0.46 % (3755655)...printing done.
% 0.17/0.46 % (3755659)...printing done.
% 0.17/0.46 % TRYING [3]
% 0.17/0.46 % (3755655)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (3755655)------------------------------
% 0.17/0.46 % (3755655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.46 % (3755655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.46 % (3755655)CaDiCaL version: 2.1.3
% 0.17/0.46 % (3755655)Termination reason: Refutation
% 0.17/0.46 % (3755655)Time elapsed: 0.013 s
% 0.17/0.46 % (3755655)Peak memory usage: 13 MB
% 0.17/0.46 % (3755655)Instructions burned: 35 (million)
% 0.17/0.46 % (3755648)Success in time 0.037 s
% 0.17/0.46 % Vampire exiting
%------------------------------------------------------------------------------