%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL950_17 : 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 : n015.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 12:01:14 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 410 ( 0 equ)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 509 ( 179 ~; 172 |; 81 &)
% ( 0 <=>; 77 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 12 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 31 ( 31 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 4 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 302 ( 257 !; 45 ?; 302 :)
% 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/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
tff(f2,axiom,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f4,axiom,
! [X0: '$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'] :
( '$ki_accessible'(X4,X5)
=> intersect(X5,X1,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
tff(f5,axiom,
! [X0: '$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'] :
( '$ki_accessible'(X4,X5)
=> intersect(X5,X1,X3) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> intersect(X5,X3,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
tff(f6,conjecture,
! [X0: '$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'] :
( '$ki_accessible'(X6,X7)
=> intersect(X7,X3,X5) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f7,negated_conjecture,
~ ! [X0: '$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'] :
( '$ki_accessible'(X9,X13)
=> intersect(X13,X1,X3) ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
tff(f9,plain,
! [X0: '$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'] :
( '$ki_accessible'(X4,X5)
=> intersect(X5,X1,X3) )
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X4,X6)
=> intersect(X6,X3,X1) ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
tff(f10,plain,
~ ! [X0: '$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'('$ki_local_world',X0) ),
inference(flattening,[],[f11]) ).
tff(f13,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ! [X4: '$ki_world'] :
( ! [X6: '$ki_world'] :
( intersect(X6,X3,X1)
| ~ '$ki_accessible'(X4,X6) )
| ? [X5: '$ki_world'] :
( ~ intersect(X5,X1,X3)
& '$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,[],[f9]) ).
tff(f14,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ! [X4: '$ki_world'] :
( ! [X6: '$ki_world'] :
( intersect(X6,X3,X1)
| ~ '$ki_accessible'(X4,X6) )
| ? [X5: '$ki_world'] :
( ~ intersect(X5,X1,X3)
& '$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,[],[f13]) ).
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'('$ki_local_world',X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X7,sK4(X1,X4,X6)),skolemize(X8,sK5(X3,X4,X6))],[f23]) ).
tff(f25,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( intersect(X5,X3,X1)
| ~ '$ki_accessible'(X4,X5) )
| ? [X6: '$ki_world'] :
( ~ intersect(X6,X1,X3)
& '$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,[],[f14]) ).
tff(f26,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( intersect(X5,X3,X1)
| ~ '$ki_accessible'(X4,X5) )
| ( ~ intersect(sK6(X1,X3,X4),X1,X3)
& '$ki_accessible'(X4,sK6(X1,X3,X4)) )
| ~ '$ki_accessible'(X2,X4) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X6,sK6(X1,X3,X4))],[f25]) ).
tff(f27,plain,
? [X0: '$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(f30,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f2]) ).
tff(f41,plain,
! [X2: '$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(f44,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X3,X1)
| ~ '$ki_accessible'(X4,X5)
| ~ intersect(sK6(X1,X3,X4),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,[],[f26]) ).
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(f80,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X3,X1)
| ~ intersect(sK6(X1,X3,X4),X1,X3)
| ~ '$ki_accessible'(X2,X4)
| ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f44,f29]) ).
tff(f81,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X3,X1)
| ~ intersect(sK6(X1,X3,X4),X1,X3)
| ~ '$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(forward_subsumption_resolution,[],[f80,f29]) ).
tff(f82,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X3,X1)
| ~ intersect(sK6(X1,X3,X4),X1,X3)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f81,f30]) ).
tff(f83,plain,
! [X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X3,X1)
| ~ intersect(sK6(X1,X3,X4),X1,X3)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f82,f29]) ).
tff(f84,plain,
! [X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X3,X1)
| ~ intersect(sK6(X1,X3,X4),X1,X3)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f83,f30]) ).
tff(f85,plain,
! [X3: $i,X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( ~ intersect(sK6(X1,X3,X4),X1,X3)
| intersect(X5,X3,X1) ),
inference(forward_subsumption_resolution,[],[f84,f29]) ).
tff(f100,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X1,X3)
| ~ '$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'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f41,f29]) ).
tff(f101,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X1,X3)
| ~ member(sK4(X1,X4,X6),X6,X1)
| ~ member(sK5(X3,X4,X6),X6,X3)
| ~ '$ki_accessible'(X2,X4)
| ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f100,f30]) ).
tff(f102,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X1,X3)
| ~ member(sK4(X1,X4,X6),X6,X1)
| ~ member(sK5(X3,X4,X6),X6,X3)
| ~ '$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(forward_subsumption_resolution,[],[f101,f29]) ).
tff(f103,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X1,X3)
| ~ member(sK4(X1,X4,X6),X6,X1)
| ~ member(sK5(X3,X4,X6),X6,X3)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f102,f30]) ).
tff(f104,plain,
! [X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X1,X3)
| ~ member(sK4(X1,X4,X6),X6,X1)
| ~ member(sK5(X3,X4,X6),X6,X3)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f103,f29]) ).
tff(f105,plain,
! [X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
( intersect(X5,X1,X3)
| ~ member(sK4(X1,X4,X6),X6,X1)
| ~ member(sK5(X3,X4,X6),X6,X3)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f104,f30]) ).
tff(f106,plain,
! [X3: $i,X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
( ~ member(sK5(X3,X4,X6),X6,X3)
| ~ member(sK4(X1,X4,X6),X6,X1)
| intersect(X5,X1,X3) ),
inference(forward_subsumption_resolution,[],[f105,f29]) ).
tff(f116,plain,
! [X2: '$ki_world',X0: $i,X1: '$ki_world'] :
( ~ member(sK4(X0,X1,sK8),sK8,X0)
| intersect(X2,X0,sK10)
| ~ '$ki_accessible'(sK13,sK5(sK10,X1,sK8)) ),
inference(resolution,[],[f106,f53]) ).
tff(f118,plain,
! [X2: '$ki_world',X0: $i,X1: '$ki_world'] :
( ~ member(sK4(X0,X1,sK8),sK8,X0)
| intersect(X2,X0,sK10) ),
inference(forward_subsumption_resolution,[],[f116,f29]) ).
tff(f209,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( intersect(X0,sK12,sK10)
| ~ '$ki_accessible'(sK13,sK4(sK12,X1,sK8)) ),
inference(resolution,[],[f118,f52]) ).
tff(f212,plain,
! [X0: '$ki_world'] : intersect(X0,sK12,sK10),
inference(forward_subsumption_resolution,[],[f209,f29]) ).
tff(f216,plain,
! [X0: '$ki_world'] : intersect(X0,sK10,sK12),
inference(resolution,[],[f212,f85]) ).
tff(f217,plain,
$false,
inference(resolution,[],[f216,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL950_17 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n015.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 17:11:31 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
% 0.12/0.45 % (1869066)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (1869073)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4015004465:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.45 % (1869073) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1869066-1869073"...
% 0.12/0.45 % (1869072)% WARNING: option uhcvi not known.
% 0.12/0.45 % (1869073)...printing done.
% 0.12/0.45 % (1869073)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (1869073)------------------------------
% 0.12/0.45 % (1869073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.45 % (1869073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.45 % (1869073)CaDiCaL version: 2.1.3
% 0.12/0.45 % (1869073)Termination reason: Refutation
% 0.12/0.45 % (1869073)Time elapsed: 0.003 s
% 0.12/0.45 % (1869073)Peak memory usage: 11 MB
% 0.12/0.45 % (1869073)Instructions burned: 7 (million)
% 0.12/0.45 % (1869066)Success in time 0.027 s
% 0.12/0.45 % Vampire exiting
%------------------------------------------------------------------------------