%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL949_4 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 11:57:17 AM UTC 2026
% Result : Theorem 2.02s 0.80s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 312 ( 0 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 403 ( 154 ~; 146 |; 53 &)
% ( 0 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 11 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 3 con; 0-3 aty)
% Number of variables : 213 ( 182 !; 31 ?; 213 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_27,type,
sK1: '$ki_world' ).
tff(func_def_29,type,
sK3: '$ki_world' ).
tff(func_def_30,type,
sK4: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_31,type,
sK5: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_32,type,
sK6: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_33,type,
sK7: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_34,type,
sK8: ( $i * $i * '$ki_world' ) > $i ).
tff(func_def_35,type,
sK9: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_36,type,
sK10: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_37,type,
sK11: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_38,type,
sK12: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_39,type,
sK13: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_40,type,
sK14: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_41,type,
sK15: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_42,type,
sK16: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_43,type,
sK17: '$ki_world' > $i ).
tff(func_def_44,type,
sK18: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_45,type,
sK19: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_46,type,
sK20: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_47,type,
sK21: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_48,type,
sK22: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_49,type,
sK23: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_50,type,
sK24: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
qmltpeq: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_3,type,
inductive: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
disjoint: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_5,type,
function: ( '$ki_world' * $i ) > $o ).
tff(pred_def_6,type,
member: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_7,type,
subclass: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_8,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(pred_def_9,type,
sP0: ( $i * $i * '$ki_world' ) > $o ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f3,axiom,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f47,axiom,
! [X0: '$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'] :
( '$ki_accessible'(X4,X5)
=> subclass(X5,X1,X3) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> ! [X6: $i] :
( '$ki_exists_in_world_$i'(X5,X6)
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X5,X7)
=> ( ! [X8: '$ki_world'] :
( '$ki_accessible'(X7,X8)
=> member(X8,X6,X1) )
=> ! [X8: '$ki_world'] :
( '$ki_accessible'(X7,X8)
=> member(X8,X6,X3) ) ) ) ) ) ) )
& ! [X4: '$ki_world'] :
( '$ki_accessible'(X2,X4)
=> ( ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> ! [X6: $i] :
( '$ki_exists_in_world_$i'(X5,X6)
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X5,X7)
=> ( ! [X8: '$ki_world'] :
( '$ki_accessible'(X7,X8)
=> member(X8,X6,X1) )
=> ! [X8: '$ki_world'] :
( '$ki_accessible'(X7,X8)
=> member(X8,X6,X3) ) ) ) ) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> subclass(X5,X1,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
tff(f88,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> subclass(X2,X1,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f89,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> subclass(X2,X1,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f88]) ).
tff(f91,plain,
! [X0: '$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'] :
( '$ki_accessible'(X4,X5)
=> subclass(X5,X1,X3) )
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X4,X6)
=> ! [X7: $i] :
( '$ki_exists_in_world_$i'(X6,X7)
=> ! [X8: '$ki_world'] :
( '$ki_accessible'(X6,X8)
=> ( ! [X9: '$ki_world'] :
( '$ki_accessible'(X8,X9)
=> member(X9,X7,X1) )
=> ! [X10: '$ki_world'] :
( '$ki_accessible'(X8,X10)
=> member(X10,X7,X3) ) ) ) ) ) ) )
& ! [X11: '$ki_world'] :
( '$ki_accessible'(X2,X11)
=> ( ! [X12: '$ki_world'] :
( '$ki_accessible'(X11,X12)
=> ! [X13: $i] :
( '$ki_exists_in_world_$i'(X12,X13)
=> ! [X14: '$ki_world'] :
( '$ki_accessible'(X12,X14)
=> ( ! [X15: '$ki_world'] :
( '$ki_accessible'(X14,X15)
=> member(X15,X13,X1) )
=> ! [X16: '$ki_world'] :
( '$ki_accessible'(X14,X16)
=> member(X16,X13,X3) ) ) ) ) )
=> ! [X17: '$ki_world'] :
( '$ki_accessible'(X11,X17)
=> subclass(X17,X1,X3) ) ) ) ) ) ) ) ),
inference(rectify,[],[f47]) ).
tff(f98,plain,
? [X0: '$ki_world'] :
( ? [X1: $i] :
( ? [X2: '$ki_world'] :
( ~ subclass(X2,X1,X1)
& '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f89]) ).
tff(f104,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ( ! [X4: '$ki_world'] :
( ! [X6: '$ki_world'] :
( ! [X7: $i] :
( ! [X8: '$ki_world'] :
( ! [X10: '$ki_world'] :
( member(X10,X7,X3)
| ~ '$ki_accessible'(X8,X10) )
| ? [X9: '$ki_world'] :
( ~ member(X9,X7,X1)
& '$ki_accessible'(X8,X9) )
| ~ '$ki_accessible'(X6,X8) )
| ~ '$ki_exists_in_world_$i'(X6,X7) )
| ~ '$ki_accessible'(X4,X6) )
| ? [X5: '$ki_world'] :
( ~ subclass(X5,X1,X3)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X2,X4) )
& ! [X11: '$ki_world'] :
( ! [X17: '$ki_world'] :
( subclass(X17,X1,X3)
| ~ '$ki_accessible'(X11,X17) )
| ? [X12: '$ki_world'] :
( ? [X13: $i] :
( ? [X14: '$ki_world'] :
( ? [X16: '$ki_world'] :
( ~ member(X16,X13,X3)
& '$ki_accessible'(X14,X16) )
& ! [X15: '$ki_world'] :
( member(X15,X13,X1)
| ~ '$ki_accessible'(X14,X15) )
& '$ki_accessible'(X12,X14) )
& '$ki_exists_in_world_$i'(X12,X13) )
& '$ki_accessible'(X11,X12) )
| ~ '$ki_accessible'(X2,X11) ) )
| ~ '$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,[],[f91]) ).
tff(f105,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ( ! [X4: '$ki_world'] :
( ! [X6: '$ki_world'] :
( ! [X7: $i] :
( ! [X8: '$ki_world'] :
( ! [X10: '$ki_world'] :
( member(X10,X7,X3)
| ~ '$ki_accessible'(X8,X10) )
| ? [X9: '$ki_world'] :
( ~ member(X9,X7,X1)
& '$ki_accessible'(X8,X9) )
| ~ '$ki_accessible'(X6,X8) )
| ~ '$ki_exists_in_world_$i'(X6,X7) )
| ~ '$ki_accessible'(X4,X6) )
| ? [X5: '$ki_world'] :
( ~ subclass(X5,X1,X3)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X2,X4) )
& ! [X11: '$ki_world'] :
( ! [X17: '$ki_world'] :
( subclass(X17,X1,X3)
| ~ '$ki_accessible'(X11,X17) )
| ? [X12: '$ki_world'] :
( ? [X13: $i] :
( ? [X14: '$ki_world'] :
( ? [X16: '$ki_world'] :
( ~ member(X16,X13,X3)
& '$ki_accessible'(X14,X16) )
& ! [X15: '$ki_world'] :
( member(X15,X13,X1)
| ~ '$ki_accessible'(X14,X15) )
& '$ki_accessible'(X12,X14) )
& '$ki_exists_in_world_$i'(X12,X13) )
& '$ki_accessible'(X11,X12) )
| ~ '$ki_accessible'(X2,X11) ) )
| ~ '$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,[],[f104]) ).
tff(f119,definition,
! [X3: $i,X1: $i,X2: '$ki_world'] :
( ! [X11: '$ki_world'] :
( ! [X17: '$ki_world'] :
( subclass(X17,X1,X3)
| ~ '$ki_accessible'(X11,X17) )
| ? [X12: '$ki_world'] :
( ? [X13: $i] :
( ? [X14: '$ki_world'] :
( ? [X16: '$ki_world'] :
( ~ member(X16,X13,X3)
& '$ki_accessible'(X14,X16) )
& ! [X15: '$ki_world'] :
( member(X15,X13,X1)
| ~ '$ki_accessible'(X14,X15) )
& '$ki_accessible'(X12,X14) )
& '$ki_exists_in_world_$i'(X12,X13) )
& '$ki_accessible'(X11,X12) )
| ~ '$ki_accessible'(X2,X11) )
| ~ sP0(X3,X1,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f120,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ( ! [X4: '$ki_world'] :
( ! [X6: '$ki_world'] :
( ! [X7: $i] :
( ! [X8: '$ki_world'] :
( ! [X10: '$ki_world'] :
( member(X10,X7,X3)
| ~ '$ki_accessible'(X8,X10) )
| ? [X9: '$ki_world'] :
( ~ member(X9,X7,X1)
& '$ki_accessible'(X8,X9) )
| ~ '$ki_accessible'(X6,X8) )
| ~ '$ki_exists_in_world_$i'(X6,X7) )
| ~ '$ki_accessible'(X4,X6) )
| ? [X5: '$ki_world'] :
( ~ subclass(X5,X1,X3)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X2,X4) )
& sP0(X3,X1,X2) )
| ~ '$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(definition_folding,[],[f105,f119]) ).
tff(f121,plain,
( ~ subclass(sK3,sK2,sK2)
& '$ki_accessible'(sK1,sK3)
& '$ki_exists_in_world_$i'(sK1,sK2)
& '$ki_accessible'('$ki_local_world',sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f98]) ).
tff(f124,plain,
! [X3: $i,X1: $i,X2: '$ki_world'] :
( ! [X11: '$ki_world'] :
( ! [X17: '$ki_world'] :
( subclass(X17,X1,X3)
| ~ '$ki_accessible'(X11,X17) )
| ? [X12: '$ki_world'] :
( ? [X13: $i] :
( ? [X14: '$ki_world'] :
( ? [X16: '$ki_world'] :
( ~ member(X16,X13,X3)
& '$ki_accessible'(X14,X16) )
& ! [X15: '$ki_world'] :
( member(X15,X13,X1)
| ~ '$ki_accessible'(X14,X15) )
& '$ki_accessible'(X12,X14) )
& '$ki_exists_in_world_$i'(X12,X13) )
& '$ki_accessible'(X11,X12) )
| ~ '$ki_accessible'(X2,X11) )
| ~ sP0(X3,X1,X2) ),
inference(nnf_transformation,[],[f119]) ).
tff(f125,plain,
! [X0: $i,X1: $i,X2: '$ki_world'] :
( ! [X3: '$ki_world'] :
( ! [X4: '$ki_world'] :
( subclass(X4,X1,X0)
| ~ '$ki_accessible'(X3,X4) )
| ? [X5: '$ki_world'] :
( ? [X6: $i] :
( ? [X7: '$ki_world'] :
( ? [X8: '$ki_world'] :
( ~ member(X8,X6,X0)
& '$ki_accessible'(X7,X8) )
& ! [X9: '$ki_world'] :
( member(X9,X6,X1)
| ~ '$ki_accessible'(X7,X9) )
& '$ki_accessible'(X5,X7) )
& '$ki_exists_in_world_$i'(X5,X6) )
& '$ki_accessible'(X3,X5) )
| ~ '$ki_accessible'(X2,X3) )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f124]) ).
tff(f126,plain,
! [X0: $i,X1: $i,X2: '$ki_world'] :
( ! [X3: '$ki_world'] :
( ! [X4: '$ki_world'] :
( subclass(X4,X1,X0)
| ~ '$ki_accessible'(X3,X4) )
| ( ~ member(sK10(X0,X1,X3),sK8(X0,X1,X3),X0)
& '$ki_accessible'(sK9(X0,X1,X3),sK10(X0,X1,X3))
& ! [X9: '$ki_world'] :
( member(X9,sK8(X0,X1,X3),X1)
| ~ '$ki_accessible'(sK9(X0,X1,X3),X9) )
& '$ki_accessible'(sK7(X0,X1,X3),sK9(X0,X1,X3))
& '$ki_exists_in_world_$i'(sK7(X0,X1,X3),sK8(X0,X1,X3))
& '$ki_accessible'(X3,sK7(X0,X1,X3)) )
| ~ '$ki_accessible'(X2,X3) )
| ~ sP0(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X5,sK7(X0,X1,X3)),skolemize(X6,sK8(X0,X1,X3)),skolemize(X7,sK9(X0,X1,X3)),skolemize(X8,sK10(X0,X1,X3))],[f125]) ).
tff(f127,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ! [X6: $i] :
( ! [X7: '$ki_world'] :
( ! [X8: '$ki_world'] :
( member(X8,X6,X3)
| ~ '$ki_accessible'(X7,X8) )
| ? [X9: '$ki_world'] :
( ~ member(X9,X6,X1)
& '$ki_accessible'(X7,X9) )
| ~ '$ki_accessible'(X5,X7) )
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'(X4,X5) )
| ? [X10: '$ki_world'] :
( ~ subclass(X10,X1,X3)
& '$ki_accessible'(X4,X10) )
| ~ '$ki_accessible'(X2,X4) )
& sP0(X3,X1,X2) )
| ~ '$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,[],[f120]) ).
tff(f128,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ! [X6: $i] :
( ! [X7: '$ki_world'] :
( ! [X8: '$ki_world'] :
( member(X8,X6,X3)
| ~ '$ki_accessible'(X7,X8) )
| ( ~ member(sK11(X1,X6,X7),X6,X1)
& '$ki_accessible'(X7,sK11(X1,X6,X7)) )
| ~ '$ki_accessible'(X5,X7) )
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'(X4,X5) )
| ( ~ subclass(sK12(X1,X3,X4),X1,X3)
& '$ki_accessible'(X4,sK12(X1,X3,X4)) )
| ~ '$ki_accessible'(X2,X4) )
& sP0(X3,X1,X2) )
| ~ '$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,[sK11,sK12]),skolemize(X9,sK11(X1,X6,X7)),skolemize(X10,sK12(X1,X3,X4))],[f127]) ).
tff(f142,plain,
'$ki_accessible'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f121]) ).
tff(f144,plain,
'$ki_accessible'(sK1,sK3),
inference(cnf_transformation,[],[f121]) ).
tff(f145,plain,
~ subclass(sK3,sK2,sK2),
inference(cnf_transformation,[],[f121]) ).
tff(f147,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f160,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: $i,X1: $i,X9: '$ki_world',X4: '$ki_world'] :
( member(X9,sK8(X0,X1,X3),X1)
| ~ '$ki_accessible'(X3,X4)
| subclass(X4,X1,X0)
| ~ '$ki_accessible'(sK9(X0,X1,X3),X9)
| ~ '$ki_accessible'(X2,X3)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f126]) ).
tff(f161,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: $i,X1: $i,X4: '$ki_world'] :
( '$ki_accessible'(sK9(X0,X1,X3),sK10(X0,X1,X3))
| ~ '$ki_accessible'(X3,X4)
| subclass(X4,X1,X0)
| ~ '$ki_accessible'(X2,X3)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f126]) ).
tff(f162,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: $i,X1: $i,X4: '$ki_world'] :
( ~ member(sK10(X0,X1,X3),sK8(X0,X1,X3),X0)
| ~ '$ki_accessible'(X3,X4)
| subclass(X4,X1,X0)
| ~ '$ki_accessible'(X2,X3)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f126]) ).
tff(f163,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i] :
( sP0(X3,X1,X2)
| ~ '$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,[],[f128]) ).
tff(f177,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f3]) ).
tff(f195,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i] :
( sP0(X3,X1,X2)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f163,f177]) ).
tff(f196,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i] :
( sP0(X3,X1,X2)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f195,f177]) ).
tff(f197,plain,
! [X2: $i,X3: '$ki_world',X0: '$ki_world',X1: '$ki_world',X4: '$ki_world',X5: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| subclass(X1,X2,X2)
| ~ '$ki_accessible'(sK9(X2,X2,X0),sK10(X2,X2,X0))
| ~ '$ki_accessible'(X3,X0)
| ~ sP0(X2,X2,X3)
| ~ '$ki_accessible'(X0,X4)
| subclass(X4,X2,X2)
| ~ '$ki_accessible'(X5,X0)
| ~ sP0(X2,X2,X5) ),
inference(resolution,[],[f160,f162]) ).
tff(f198,plain,
! [X2: $i,X3: '$ki_world',X0: '$ki_world',X1: '$ki_world',X4: '$ki_world',X5: '$ki_world'] :
( subclass(X4,X2,X2)
| subclass(X1,X2,X2)
| ~ '$ki_accessible'(X3,X0)
| ~ sP0(X2,X2,X3)
| ~ '$ki_accessible'(X0,X4)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(X5,X0)
| ~ sP0(X2,X2,X5) ),
inference(forward_subsumption_resolution,[],[f197,f161]) ).
tff(f329,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( subclass(X0,sK2,sK2)
| ~ '$ki_accessible'(X1,X2)
| ~ sP0(sK2,sK2,X1)
| ~ '$ki_accessible'(X2,sK3)
| ~ '$ki_accessible'(X2,X0)
| ~ '$ki_accessible'(X3,X2)
| ~ sP0(sK2,sK2,X3) ),
inference(resolution,[],[f198,f145]) ).
tff(f339,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| ~ sP0(sK2,sK2,X0)
| ~ '$ki_accessible'(X1,sK3)
| ~ '$ki_accessible'(X1,sK3)
| ~ '$ki_accessible'(X2,X1)
| ~ sP0(sK2,sK2,X2) ),
inference(resolution,[],[f329,f145]) ).
tff(f343,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ sP0(sK2,sK2,X2)
| ~ sP0(sK2,sK2,X0)
| ~ '$ki_accessible'(X1,sK3)
| ~ '$ki_accessible'(X2,X1)
| ~ '$ki_accessible'(X0,X1) ),
inference(duplicate_literal_removal,[],[f339]) ).
tff(f345,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ sP0(sK2,sK2,X0)
| ~ '$ki_accessible'(X1,sK3)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(X0,X1) ),
inference(factoring,[],[f343]) ).
tff(f346,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ sP0(sK2,sK2,X0)
| ~ '$ki_accessible'(X1,sK3)
| ~ '$ki_accessible'(X0,X1) ),
inference(duplicate_literal_removal,[],[f345]) ).
tff(f350,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_accessible'(X2,X1)
| ~ '$ki_accessible'(X0,sK3) ),
inference(resolution,[],[f346,f196]) ).
tff(f370,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world','$ki_local_world')
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK3) ),
inference(factoring,[],[f350]) ).
tff(f372,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f370,f147]) ).
tff(f373,plain,
~ '$ki_accessible'(sK1,sK3),
inference(resolution,[],[f372,f142]) ).
tff(f385,plain,
$false,
inference(forward_subsumption_resolution,[],[f373,f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL949_4 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 17:07:49 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.33 Running first-order theorem proving
% 0.04/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.28/0.80 % (2599125)Detected formulas, will run a generic FOF schedule.
% 0.28/0.80 % (2599199)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=645410413:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.28/0.80 % (2599202)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4066456291:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.28/0.80 % (2599201)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2140843168:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.28/0.80 % (2599196)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4206218304:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.28/0.80 % (2599197)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3108398625:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.28/0.80 % (2599200)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3071688514:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.28/0.80 % (2599201)First to succeed.
% 0.28/0.80 % (2599201)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2599125"
% 0.28/0.80 % (2599200)Refutation not found, incomplete strategy
% 0.28/0.80 % (2599200)------------------------------
% 0.28/0.80 % (2599200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.28/0.80 % (2599200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.80 % (2599200)CaDiCaL version: 2.1.3
% 0.28/0.80 % (2599200)Termination reason: Refutation not found, incomplete strategy
% 0.28/0.80 % (2599200)Time elapsed: 0.005 s
% 0.28/0.80 % (2599200)Peak memory usage: 88 MB
% 0.28/0.80 % (2599200)Instructions burned: 16 (million)
% 0.28/0.80 % (2599202)Also succeeded, but the first one will report.
% 0.28/0.80 % (2599203)dis-21_1_sil=8000:lcm=predicate:random_seed=724428032:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.02/0.80 % (2599203)Also succeeded, but the first one will report.
% 2.02/0.80 % (2599200)------------------------------
% 2.02/0.80 % (2599200)------------------------------
% 2.02/0.80 % (2599201)Refutation found. Thanks to Tanya!
% 2.02/0.80 % SZS status Theorem for theBenchmark
% 2.02/0.80 % SZS output start Proof for theBenchmark
% See solution above
% 2.02/0.89 % (2599201)------------------------------
% 2.02/0.89 % (2599201)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.02/0.89 % (2599201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.89 % (2599201)CaDiCaL version: 2.1.3
% 2.02/0.89 % (2599201)Termination reason: Refutation
% 2.02/0.89 % (2599201)Time elapsed: 0.007 s
% 2.02/0.89 % (2599201)Peak memory usage: 88 MB
% 2.02/0.89 % (2599201)Instructions burned: 22 (million)
% 2.02/0.89 % (2599201)------------------------------
% 2.02/0.89 % (2599201)------------------------------
% 2.02/0.89 % (2599125)Success in time 0.262 s
% 2.02/0.89 % Vampire exiting
%------------------------------------------------------------------------------