%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL950_17 : 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 : n013.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 0.87s 1.68s
% Output : Refutation 5.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 77 ( 23 unt; 0 typ; 9 def)
% Number of atoms : 440 ( 0 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 474 ( 172 ~; 156 |; 77 &)
% ( 8 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 61 ( 61 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 16 usr; 12 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 183 ( 0 sgn 141 !; 42 ?; 183 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_1,type,
sK1: '$ki_world' > $i ).
tff(func_def_2,type,
sK2: ( $i * $i * '$ki_world' ) > $i ).
tff(func_def_3,type,
sK3: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_4,type,
sK4: ( $i * '$ki_world' * $i ) > '$ki_world' ).
tff(func_def_5,type,
sK5: ( $i * '$ki_world' * $i ) > '$ki_world' ).
tff(func_def_6,type,
sK6: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_7,type,
sK7: '$ki_world' ).
tff(func_def_9,type,
sK9: '$ki_world' ).
tff(func_def_11,type,
sK11: '$ki_world' ).
tff(func_def_13,type,
sK13: '$ki_world' ).
tff(func_def_14,type,
sK14: '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
intersect: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_3,type,
member: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_4,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(pred_def_5,type,
sP0: ( $i * $i * '$ki_world' ) > $o ).
tff(f1,axiom,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
tff(f4,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)
=> intersect(X5,X1,X3) )
=> ? [X6: $i] :
( '$ki_exists_in_world_$i'(X4,X6)
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> member(X5,X6,X1) )
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> member(X5,X6,X3) ) ) ) )
& ! [X4: '$ki_world'] :
( '$ki_accessible'(X2,X4)
=> ( ? [X6: $i] :
( '$ki_exists_in_world_$i'(X4,X6)
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> member(X5,X6,X1) )
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> member(X5,X6,X3) ) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> intersect(X5,X1,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
tff(f6,conjecture,
! [X0: '$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: $i] :
( '$ki_exists_in_world_$i'(X4,X5)
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X4,X6)
=> ( ( ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> member(X7,X1,X3) )
& ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> member(X7,X1,X5) ) )
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> intersect(X7,X3,X5) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f7,negated_conjecture,
~ ! [X0: '$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: $i] :
( '$ki_exists_in_world_$i'(X4,X5)
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X4,X6)
=> ( ( ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> member(X7,X1,X3) )
& ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> member(X7,X1,X5) ) )
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> intersect(X7,X3,X5) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
! [X0: '$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)
=> intersect(X5,X1,X3) )
=> ? [X6: $i] :
( '$ki_exists_in_world_$i'(X4,X6)
& ! [X7: '$ki_world'] :
( '$ki_accessible'(X4,X7)
=> member(X7,X6,X1) )
& ! [X8: '$ki_world'] :
( '$ki_accessible'(X4,X8)
=> member(X8,X6,X3) ) ) ) )
& ! [X9: '$ki_world'] :
( '$ki_accessible'(X2,X9)
=> ( ? [X10: $i] :
( '$ki_exists_in_world_$i'(X9,X10)
& ! [X11: '$ki_world'] :
( '$ki_accessible'(X9,X11)
=> member(X11,X10,X1) )
& ! [X12: '$ki_world'] :
( '$ki_accessible'(X9,X12)
=> member(X12,X10,X3) ) )
=> ! [X13: '$ki_world'] :
( '$ki_accessible'(X9,X13)
=> intersect(X13,X1,X3) ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
tff(f10,plain,
~ ! [X0: '$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: $i] :
( '$ki_exists_in_world_$i'(X4,X5)
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X4,X6)
=> ( ( ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> member(X7,X1,X3) )
& ! [X8: '$ki_world'] :
( '$ki_accessible'(X6,X8)
=> member(X8,X1,X5) ) )
=> ! [X9: '$ki_world'] :
( '$ki_accessible'(X6,X9)
=> intersect(X9,X3,X5) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
tff(f11,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ( ! [X4: '$ki_world'] :
( ? [X6: $i] :
( '$ki_exists_in_world_$i'(X4,X6)
& ! [X7: '$ki_world'] :
( member(X7,X6,X1)
| ~ '$ki_accessible'(X4,X7) )
& ! [X8: '$ki_world'] :
( member(X8,X6,X3)
| ~ '$ki_accessible'(X4,X8) ) )
| ? [X5: '$ki_world'] :
( ~ intersect(X5,X1,X3)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X2,X4) )
& ! [X9: '$ki_world'] :
( ! [X13: '$ki_world'] :
( intersect(X13,X1,X3)
| ~ '$ki_accessible'(X9,X13) )
| ! [X10: $i] :
( ~ '$ki_exists_in_world_$i'(X9,X10)
| ? [X11: '$ki_world'] :
( ~ member(X11,X10,X1)
& '$ki_accessible'(X9,X11) )
| ? [X12: '$ki_world'] :
( ~ member(X12,X10,X3)
& '$ki_accessible'(X9,X12) ) )
| ~ '$ki_accessible'(X2,X9) ) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f8]) ).
tff(f12,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ( ! [X4: '$ki_world'] :
( ? [X6: $i] :
( '$ki_exists_in_world_$i'(X4,X6)
& ! [X7: '$ki_world'] :
( member(X7,X6,X1)
| ~ '$ki_accessible'(X4,X7) )
& ! [X8: '$ki_world'] :
( member(X8,X6,X3)
| ~ '$ki_accessible'(X4,X8) ) )
| ? [X5: '$ki_world'] :
( ~ intersect(X5,X1,X3)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X2,X4) )
& ! [X9: '$ki_world'] :
( ! [X13: '$ki_world'] :
( intersect(X13,X1,X3)
| ~ '$ki_accessible'(X9,X13) )
| ! [X10: $i] :
( ~ '$ki_exists_in_world_$i'(X9,X10)
| ? [X11: '$ki_world'] :
( ~ member(X11,X10,X1)
& '$ki_accessible'(X9,X11) )
| ? [X12: '$ki_world'] :
( ~ member(X12,X10,X3)
& '$ki_accessible'(X9,X12) ) )
| ~ '$ki_accessible'(X2,X9) ) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f11]) ).
tff(f15,plain,
? [X0: '$ki_world'] :
( ? [X1: $i] :
( ? [X2: '$ki_world'] :
( ? [X3: $i] :
( ? [X4: '$ki_world'] :
( ? [X5: $i] :
( ? [X6: '$ki_world'] :
( ? [X9: '$ki_world'] :
( ~ intersect(X9,X3,X5)
& '$ki_accessible'(X6,X9) )
& ! [X7: '$ki_world'] :
( member(X7,X1,X3)
| ~ '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,X1,X5)
| ~ '$ki_accessible'(X6,X8) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f10]) ).
tff(f16,plain,
? [X0: '$ki_world'] :
( ? [X1: $i] :
( ? [X2: '$ki_world'] :
( ? [X3: $i] :
( ? [X4: '$ki_world'] :
( ? [X5: $i] :
( ? [X6: '$ki_world'] :
( ? [X9: '$ki_world'] :
( ~ intersect(X9,X3,X5)
& '$ki_accessible'(X6,X9) )
& ! [X7: '$ki_world'] :
( member(X7,X1,X3)
| ~ '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,X1,X5)
| ~ '$ki_accessible'(X6,X8) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$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,[],[f15]) ).
tff(f17,definition,
! [X1: $i,X3: $i,X2: '$ki_world'] :
( ! [X4: '$ki_world'] :
( ? [X6: $i] :
( '$ki_exists_in_world_$i'(X4,X6)
& ! [X7: '$ki_world'] :
( member(X7,X6,X1)
| ~ '$ki_accessible'(X4,X7) )
& ! [X8: '$ki_world'] :
( member(X8,X6,X3)
| ~ '$ki_accessible'(X4,X8) ) )
| ? [X5: '$ki_world'] :
( ~ intersect(X5,X1,X3)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X2,X4) )
| ~ sP0(X1,X3,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f18,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ( sP0(X1,X3,X2)
& ! [X9: '$ki_world'] :
( ! [X13: '$ki_world'] :
( intersect(X13,X1,X3)
| ~ '$ki_accessible'(X9,X13) )
| ! [X10: $i] :
( ~ '$ki_exists_in_world_$i'(X9,X10)
| ? [X11: '$ki_world'] :
( ~ member(X11,X10,X1)
& '$ki_accessible'(X9,X11) )
| ? [X12: '$ki_world'] :
( ~ member(X12,X10,X3)
& '$ki_accessible'(X9,X12) ) )
| ~ '$ki_accessible'(X2,X9) ) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(definition_folding,[],[f12,f17]) ).
tff(f23,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ( sP0(X1,X3,X2)
& ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( intersect(X5,X1,X3)
| ~ '$ki_accessible'(X4,X5) )
| ! [X6: $i] :
( ~ '$ki_exists_in_world_$i'(X4,X6)
| ? [X7: '$ki_world'] :
( ~ member(X7,X6,X1)
& '$ki_accessible'(X4,X7) )
| ? [X8: '$ki_world'] :
( ~ member(X8,X6,X3)
& '$ki_accessible'(X4,X8) ) )
| ~ '$ki_accessible'(X2,X4) ) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(rectify,[],[f18]) ).
tff(f24,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ( sP0(X1,X3,X2)
& ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( intersect(X5,X1,X3)
| ~ '$ki_accessible'(X4,X5) )
| ! [X6: $i] :
( ~ '$ki_exists_in_world_$i'(X4,X6)
| ( ~ member(sK4(X1,X4,X6),X6,X1)
& '$ki_accessible'(X4,sK4(X1,X4,X6)) )
| ( ~ member(sK5(X3,X4,X6),X6,X3)
& '$ki_accessible'(X4,sK5(X3,X4,X6)) ) )
| ~ '$ki_accessible'(X2,X4) ) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X7,sK4(X1,X4,X6)),skolemize(X8,sK5(X3,X4,X6))],[f23]) ).
tff(f27,plain,
? [X0: '$ki_world'] :
( ? [X1: $i] :
( ? [X2: '$ki_world'] :
( ? [X3: $i] :
( ? [X4: '$ki_world'] :
( ? [X5: $i] :
( ? [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ intersect(X7,X3,X5)
& '$ki_accessible'(X6,X7) )
& ! [X8: '$ki_world'] :
( member(X8,X1,X3)
| ~ '$ki_accessible'(X6,X8) )
& ! [X9: '$ki_world'] :
( member(X9,X1,X5)
| ~ '$ki_accessible'(X6,X9) )
& '$ki_accessible'(X4,X6) )
& '$ki_exists_in_world_$i'(X4,X5) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(rectify,[],[f16]) ).
tff(f28,plain,
( ~ intersect(sK14,sK10,sK12)
& '$ki_accessible'(sK13,sK14)
& ! [X8: '$ki_world'] :
( member(X8,sK8,sK10)
| ~ '$ki_accessible'(sK13,X8) )
& ! [X9: '$ki_world'] :
( member(X9,sK8,sK12)
| ~ '$ki_accessible'(sK13,X9) )
& '$ki_accessible'(sK11,sK13)
& '$ki_exists_in_world_$i'(sK11,sK12)
& '$ki_accessible'(sK9,sK11)
& '$ki_exists_in_world_$i'(sK9,sK10)
& '$ki_accessible'(sK7,sK9)
& '$ki_exists_in_world_$i'(sK7,sK8)
& '$ki_accessible'('$ki_local_world',sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10),skolemize(X4,sK11),skolemize(X5,sK12),skolemize(X6,sK13),skolemize(X7,sK14)],[f27]) ).
tff(f29,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f1]) ).
tff(f41,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X1,X3)
| ~ '$ki_accessible'(X4,X5)
| ~ '$ki_exists_in_world_$i'(X4,X6)
| ~ member(sK4(X1,X4,X6),X6,X1)
| ~ member(sK5(X3,X4,X6),X6,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,[],[f24]) ).
tff(f46,plain,
'$ki_exists_in_world_$i'(sK7,sK8),
inference(cnf_transformation,[],[f28]) ).
tff(f48,plain,
'$ki_exists_in_world_$i'(sK9,sK10),
inference(cnf_transformation,[],[f28]) ).
tff(f49,plain,
'$ki_accessible'(sK9,sK11),
inference(cnf_transformation,[],[f28]) ).
tff(f50,plain,
'$ki_exists_in_world_$i'(sK11,sK12),
inference(cnf_transformation,[],[f28]) ).
tff(f52,plain,
! [X9: '$ki_world'] :
( member(X9,sK8,sK12)
| ~ '$ki_accessible'(sK13,X9) ),
inference(cnf_transformation,[],[f28]) ).
tff(f53,plain,
! [X8: '$ki_world'] :
( member(X8,sK8,sK10)
| ~ '$ki_accessible'(sK13,X8) ),
inference(cnf_transformation,[],[f28]) ).
tff(f55,plain,
~ intersect(sK14,sK10,sK12),
inference(cnf_transformation,[],[f28]) ).
tff(f62,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ member(sK5(sK12,X0,X1),X1,sK12)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ member(sK4(sK10,X0,X1),X1,sK10)
| ~ '$ki_accessible'(X0,sK14)
| ~ '$ki_accessible'(X2,X0)
| ~ '$ki_exists_in_world_$i'(X2,sK12)
| ~ '$ki_accessible'(X3,X2)
| ~ '$ki_exists_in_world_$i'(X3,sK10)
| ~ '$ki_accessible'('$ki_local_world',X3) ),
inference(resolution,[],[f41,f55]) ).
tff(f66,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ member(sK4(sK10,X0,sK8),sK8,sK10)
| ~ '$ki_exists_in_world_$i'(X0,sK8)
| ~ '$ki_accessible'(X0,sK14)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,sK12)
| ~ '$ki_accessible'(X2,X1)
| ~ '$ki_exists_in_world_$i'(X2,sK10)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(sK13,sK5(sK12,X0,sK8)) ),
inference(resolution,[],[f62,f52]) ).
tff(f68,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK8)
| ~ '$ki_exists_in_world_$i'(X1,sK12)
| ~ '$ki_exists_in_world_$i'(X2,sK10)
| ~ '$ki_accessible'(X0,sK14)
| ~ '$ki_accessible'(X2,X1)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(sK13,sK5(sK12,X0,sK8))
| ~ '$ki_accessible'(sK13,sK4(sK10,X0,sK8)) ),
inference(resolution,[],[f66,f53]) ).
tff(f71,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK12)
| ~ '$ki_exists_in_world_$i'(X1,sK10)
| ~ '$ki_accessible'(sK7,sK14)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_accessible'(X0,sK7)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(sK13,sK5(sK12,sK7,sK8))
| ~ '$ki_accessible'(sK13,sK4(sK10,sK7,sK8)) ),
inference(resolution,[],[f68,f46]) ).
tff(f77,definition,
( spl15_1
<=> '$ki_accessible'('$ki_local_world',sK9) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
tff(f78,plain,
( ~ '$ki_accessible'('$ki_local_world',sK9)
| spl15_1 ),
inference(avatar_component_clause,[],[f77]) ).
tff(f84,definition,
( spl15_3
<=> ! [X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X1,sK10)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,sK11) ) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
tff(f85,plain,
( ! [X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X1,sK10)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,sK11) )
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f84]) ).
tff(f91,definition,
( spl15_5
<=> '$ki_accessible'(sK13,sK4(sK10,sK7,sK8)) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
tff(f92,plain,
( ~ '$ki_accessible'(sK13,sK4(sK10,sK7,sK8))
| spl15_5 ),
inference(avatar_component_clause,[],[f91]) ).
tff(f94,definition,
( spl15_6
<=> '$ki_accessible'(sK13,sK5(sK12,sK7,sK8)) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
tff(f95,plain,
( ~ '$ki_accessible'(sK13,sK5(sK12,sK7,sK8))
| spl15_6 ),
inference(avatar_component_clause,[],[f94]) ).
tff(f97,definition,
( spl15_7
<=> '$ki_accessible'(sK7,sK14) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
tff(f98,plain,
( ~ '$ki_accessible'(sK7,sK14)
| spl15_7 ),
inference(avatar_component_clause,[],[f97]) ).
tff(f100,definition,
( spl15_8
<=> ! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK12)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X0,sK7)
| ~ '$ki_exists_in_world_$i'(X1,sK10)
| ~ '$ki_accessible'(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).
tff(f101,plain,
( ! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK12)
| ~ '$ki_exists_in_world_$i'(X1,sK10)
| ~ '$ki_accessible'(X0,sK7)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,X0) )
| ~ spl15_8 ),
inference(avatar_component_clause,[],[f100]) ).
tff(f102,plain,
( ~ spl15_5
| ~ spl15_6
| ~ spl15_7
| spl15_8 ),
inference(avatar_split_clause,[],[f71,f100,f97,f94,f91]) ).
tff(f103,plain,
( $false
| spl15_1 ),
inference(resolution,[],[f78,f29]) ).
tff(f104,plain,
spl15_1,
inference(avatar_contradiction_clause,[],[f103]) ).
tff(f105,plain,
( $false
| spl15_7 ),
inference(resolution,[],[f98,f29]) ).
tff(f106,plain,
spl15_7,
inference(avatar_contradiction_clause,[],[f105]) ).
tff(f107,plain,
( $false
| spl15_5 ),
inference(resolution,[],[f92,f29]) ).
tff(f108,plain,
spl15_5,
inference(avatar_contradiction_clause,[],[f107]) ).
tff(f109,plain,
( $false
| spl15_6 ),
inference(resolution,[],[f95,f29]) ).
tff(f110,plain,
spl15_6,
inference(avatar_contradiction_clause,[],[f109]) ).
tff(f112,plain,
( ~ '$ki_accessible'('$ki_local_world',sK9)
| ~ '$ki_accessible'(sK9,sK11)
| ~ spl15_3 ),
inference(resolution,[],[f85,f48]) ).
tff(f114,definition,
( spl15_9
<=> '$ki_accessible'(sK9,sK11) ),
introduced(definition,[new_symbols(definition,[spl15_9])],[avatar_definition]) ).
tff(f115,plain,
( ~ '$ki_accessible'(sK9,sK11)
| spl15_9 ),
inference(avatar_component_clause,[],[f114]) ).
tff(f116,plain,
( ~ spl15_9
| ~ spl15_1
| ~ spl15_3 ),
inference(avatar_split_clause,[],[f112,f84,f77,f114]) ).
tff(f118,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK10)
| ~ '$ki_accessible'(sK11,sK7)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK11) )
| ~ spl15_8 ),
inference(resolution,[],[f101,f50]) ).
tff(f125,plain,
( $false
| spl15_9 ),
inference(resolution,[],[f115,f49]) ).
tff(f128,plain,
spl15_9,
inference(avatar_contradiction_clause,[],[f125]) ).
tff(f130,definition,
( spl15_11
<=> '$ki_accessible'(sK11,sK7) ),
introduced(definition,[new_symbols(definition,[spl15_11])],[avatar_definition]) ).
tff(f131,plain,
( ~ '$ki_accessible'(sK11,sK7)
| spl15_11 ),
inference(avatar_component_clause,[],[f130]) ).
tff(f132,plain,
( ~ spl15_11
| spl15_3
| ~ spl15_8 ),
inference(avatar_split_clause,[],[f118,f100,f84,f130]) ).
tff(f136,plain,
( $false
| spl15_11 ),
inference(resolution,[],[f131,f29]) ).
tff(f137,plain,
spl15_11,
inference(avatar_contradiction_clause,[],[f136]) ).
cnf(s3,plain,
( ~ spl15_5
| ~ spl15_6
| ~ spl15_7
| spl15_8 ),
inference(sat_conversion,[],[f102]) ).
cnf(s4,plain,
spl15_1,
inference(sat_conversion,[],[f104]) ).
cnf(s5,plain,
spl15_7,
inference(sat_conversion,[],[f106]) ).
cnf(s6,plain,
spl15_5,
inference(sat_conversion,[],[f108]) ).
cnf(s7,plain,
spl15_6,
inference(sat_conversion,[],[f110]) ).
cnf(s8,plain,
( ~ spl15_1
| ~ spl15_3
| ~ spl15_9 ),
inference(sat_conversion,[],[f116]) ).
cnf(s11,plain,
spl15_9,
inference(sat_conversion,[],[f128]) ).
cnf(s12,plain,
( spl15_3
| ~ spl15_8
| ~ spl15_11 ),
inference(sat_conversion,[],[f132]) ).
cnf(s14,plain,
spl15_11,
inference(sat_conversion,[],[f137]) ).
cnf(s16,plain,
( spl15_3
| ~ spl15_8 ),
inference(rat,[],[s12,s14]) ).
cnf(s17,plain,
( ~ spl15_1
| ~ spl15_3 ),
inference(rat,[],[s8,s11]) ).
cnf(s19,plain,
~ spl15_3,
inference(rat,[],[s17,s4]) ).
cnf(s20,plain,
~ spl15_8,
inference(rat,[],[s16,s19]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s3,s20,s5,s7,s6]) ).
tff(f138,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL950_17 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n013.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 17:07:37 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.45 Running first-order theorem proving
% 0.15/0.45 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
% 0.87/1.68 % (428036)Detected formulas, will run a generic FOF schedule.
% 0.87/1.68 % (428055)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=3268442957:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.87/1.68 % (428060)dis-21_1_sil=8000:lcm=predicate:random_seed=1294382932: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)
% 0.87/1.68 % (428060)First to succeed.
% 0.87/1.68 % (428060)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-428036"
% 0.87/1.68 % (428054)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=4031938285:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.87/1.68 % (428059)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4119289106:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.87/1.68 % (428058)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1634289195:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.87/1.68 % (428057)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2327591716:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.87/1.68 % (428056)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=1770890111:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.87/1.68 % (428058)Also succeeded, but the first one will report.
% 0.87/1.68 % (428059)Also succeeded, but the first one will report.
% 0.87/1.68 % (428057)Refutation not found, incomplete strategy
% 0.87/1.68 % (428057)------------------------------
% 0.87/1.68 % (428057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.87/1.68 % (428057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/1.68 % (428057)CaDiCaL version: 2.1.3
% 0.87/1.68 % (428057)Termination reason: Refutation not found, incomplete strategy
% 0.87/1.68 % (428057)Time elapsed: 0.009 s
% 0.87/1.68 % (428057)Peak memory usage: 88 MB
% 0.87/1.68 % (428057)Instructions burned: 7 (million)
% 0.87/1.68 % (428060)Refutation found. Thanks to Tanya!
% 0.87/1.68 % SZS status Theorem for theBenchmark
% 0.87/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 5.05/1.90 % (428060)------------------------------
% 5.05/1.90 % (428060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.05/1.90 % (428060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.05/1.90 % (428060)CaDiCaL version: 2.1.3
% 5.05/1.90 % (428060)Termination reason: Refutation
% 5.05/1.90 % (428060)Time elapsed: 0.006 s
% 5.05/1.90 % (428060)Peak memory usage: 89 MB
% 5.05/1.90 % (428060)Instructions burned: 7 (million)
% 5.05/1.90 % (428060)------------------------------
% 5.05/1.90 % (428060)------------------------------
% 5.05/1.90 % (428036)Success in time 0.58 s
% 5.05/1.90 % Vampire exiting
%------------------------------------------------------------------------------