%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n017.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 11:57:18 AM UTC 2026
% Result : Theorem 2.54s 1.18s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 2
% Syntax : Number of formulae : 41 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 373 ( 0 equ)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 424 ( 181 ~; 162 |; 36 &)
% ( 0 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 11 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 89 ( 89 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 161 ( 137 !; 24 ?; 161 :)
% 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' ).
tff(func_def_4,type,
sK2: '$ki_world' ).
tff(func_def_6,type,
sK4: '$ki_world' ).
tff(func_def_7,type,
sK5: '$ki_world' ).
tff(func_def_8,type,
sK6: '$ki_world' > '$ki_world' ).
tff(func_def_9,type,
sK7: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_10,type,
sK8: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_11,type,
sK9: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_12,type,
sK10: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_13,type,
sK11: '$ki_world' > $i ).
tff(pred_def_1,type,
'$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'] :
( '$ki_accessible'(X4,X5)
=> disjoint(X5,singleton(X1),X3) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
tff(f10,plain,
~ ! [X0: '$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'] :
( '$ki_accessible'(X2,X4)
=> ( ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> ~ ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> in(X6,X1,X3) ) )
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X4,X7)
=> disjoint(X7,singleton(X1),X3) ) ) ) ) ) ) ),
inference(rectify,[],[f9]) ).
tff(f11,plain,
! [X0: '$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'] :
( '$ki_accessible'(X4,X7)
=> disjoint(X7,singleton(X1),X3) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
tff(f14,plain,
? [X0: '$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,[],[f10]) ).
tff(f15,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,[],[f14]) ).
tff(f16,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,[],[f11]) ).
tff(f17,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,[],[f16]) ).
tff(f22,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,[],[f15]) ).
tff(f23,plain,
( ~ disjoint(sK5,singleton(sK1),sK3)
& '$ki_accessible'(sK4,sK5)
& ! [X6: '$ki_world'] :
( ( ~ in(sK6(X6),sK1,sK3)
& '$ki_accessible'(X6,sK6(X6)) )
| ~ '$ki_accessible'(sK4,X6) )
& '$ki_accessible'(sK2,sK4)
& '$ki_exists_in_world_$i'(sK2,sK3)
& '$ki_accessible'(sK0,sK2)
& '$ki_exists_in_world_$i'(sK0,sK1)
& '$ki_accessible'('$ki_local_world',sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X7,sK6(X6))],[f22]) ).
tff(f24,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,[],[f17]) ).
tff(f25,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'('$ki_local_world',X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X6,sK7(X1,X3,X4))],[f24]) ).
tff(f31,plain,
'$ki_accessible'('$ki_local_world',sK0),
inference(cnf_transformation,[],[f23]) ).
tff(f32,plain,
'$ki_exists_in_world_$i'(sK0,sK1),
inference(cnf_transformation,[],[f23]) ).
tff(f33,plain,
'$ki_accessible'(sK0,sK2),
inference(cnf_transformation,[],[f23]) ).
tff(f34,plain,
'$ki_exists_in_world_$i'(sK2,sK3),
inference(cnf_transformation,[],[f23]) ).
tff(f35,plain,
'$ki_accessible'(sK2,sK4),
inference(cnf_transformation,[],[f23]) ).
tff(f36,plain,
! [X6: '$ki_world'] :
( '$ki_accessible'(X6,sK6(X6))
| ~ '$ki_accessible'(sK4,X6) ),
inference(cnf_transformation,[],[f23]) ).
tff(f37,plain,
! [X6: '$ki_world'] :
( ~ in(sK6(X6),sK1,sK3)
| ~ '$ki_accessible'(sK4,X6) ),
inference(cnf_transformation,[],[f23]) ).
tff(f38,plain,
'$ki_accessible'(sK4,sK5),
inference(cnf_transformation,[],[f23]) ).
tff(f39,plain,
~ disjoint(sK5,singleton(sK1),sK3),
inference(cnf_transformation,[],[f23]) ).
tff(f41,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( '$ki_accessible'(X4,sK7(X1,X3,X4))
| ~ '$ki_accessible'(X4,X5)
| disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X2,X4)
| ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f25]) ).
tff(f42,plain,
! [X2: '$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,[],[f25]) ).
tff(f51,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: '$ki_world',X4: '$ki_world',X5: '$ki_world'] :
( in(sK6(sK7(X2,X3,X0)),X2,X3)
| ~ '$ki_accessible'(X0,X1)
| 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)
| ~ '$ki_accessible'(sK4,sK7(X2,X3,X0)) ),
inference(resolution,[],[f42,f36]) ).
tff(f57,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| disjoint(X1,singleton(sK1),sK3)
| ~ '$ki_accessible'(X2,X0)
| ~ '$ki_exists_in_world_$i'(X2,sK3)
| ~ '$ki_accessible'(X3,X2)
| ~ '$ki_exists_in_world_$i'(X3,sK1)
| ~ '$ki_accessible'('$ki_local_world',X3)
| ~ '$ki_accessible'(sK4,sK7(sK1,sK3,X0))
| ~ '$ki_accessible'(sK4,sK7(sK1,sK3,X0)) ),
inference(resolution,[],[f51,f37]) ).
tff(f58,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(sK4,sK7(sK1,sK3,X0))
| disjoint(X1,singleton(sK1),sK3)
| ~ '$ki_accessible'(X2,X0)
| ~ '$ki_exists_in_world_$i'(X2,sK3)
| ~ '$ki_accessible'(X3,X2)
| ~ '$ki_exists_in_world_$i'(X3,sK1)
| ~ '$ki_accessible'('$ki_local_world',X3)
| ~ '$ki_accessible'(X0,X1) ),
inference(duplicate_literal_removal,[],[f57]) ).
tff(f59,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world',X4: '$ki_world',X5: '$ki_world'] :
( disjoint(X3,singleton(sK1),sK3)
| ~ '$ki_accessible'(X1,sK4)
| ~ '$ki_exists_in_world_$i'(X1,sK3)
| ~ '$ki_accessible'(X2,X1)
| ~ '$ki_exists_in_world_$i'(X2,sK1)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(sK4,X0)
| ~ '$ki_accessible'(sK4,X3)
| disjoint(X0,singleton(sK1),sK3)
| ~ '$ki_accessible'(X4,sK4)
| ~ '$ki_exists_in_world_$i'(X4,sK3)
| ~ '$ki_accessible'(X5,X4)
| ~ '$ki_exists_in_world_$i'(X5,sK1)
| ~ '$ki_accessible'('$ki_local_world',X5) ),
inference(resolution,[],[f58,f41]) ).
tff(f64,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world',X4: '$ki_world'] :
( ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(sK4,X2)
| ~ '$ki_accessible'(sK4,sK5)
| disjoint(X2,singleton(sK1),sK3)
| ~ '$ki_accessible'(X3,sK4)
| ~ '$ki_exists_in_world_$i'(X3,sK3)
| ~ '$ki_accessible'(X4,X3)
| ~ '$ki_exists_in_world_$i'(X4,sK1)
| ~ '$ki_accessible'('$ki_local_world',X4) ),
inference(resolution,[],[f59,f39]) ).
tff(f66,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world',X4: '$ki_world'] :
( disjoint(X2,singleton(sK1),sK3)
| ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(sK4,X2)
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_accessible'(X3,sK4)
| ~ '$ki_exists_in_world_$i'(X3,sK3)
| ~ '$ki_accessible'(X4,X3)
| ~ '$ki_exists_in_world_$i'(X4,sK1)
| ~ '$ki_accessible'('$ki_local_world',X4) ),
inference(forward_subsumption_resolution,[],[f64,f38]) ).
tff(f69,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(sK4,sK5)
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_accessible'(X2,sK4)
| ~ '$ki_exists_in_world_$i'(X2,sK3)
| ~ '$ki_accessible'(X3,X2)
| ~ '$ki_exists_in_world_$i'(X3,sK1)
| ~ '$ki_accessible'('$ki_local_world',X3) ),
inference(resolution,[],[f66,f39]) ).
tff(f71,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X3,sK1)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_accessible'(X2,sK4)
| ~ '$ki_exists_in_world_$i'(X2,sK3)
| ~ '$ki_accessible'(X3,X2)
| ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'('$ki_local_world',X3) ),
inference(forward_subsumption_resolution,[],[f69,f38]) ).
tff(f74,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X1,sK4)
| ~ '$ki_accessible'(X2,sK4)
| ~ '$ki_exists_in_world_$i'(X2,sK3)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X1,sK3)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(factoring,[],[f71]) ).
tff(f75,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X2,sK3)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X1,sK4)
| ~ '$ki_accessible'(X2,sK4)
| ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X1,sK3) ),
inference(duplicate_literal_removal,[],[f74]) ).
tff(f78,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'(X1,X0) ),
inference(factoring,[],[f75]) ).
tff(f79,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_exists_in_world_$i'(X0,sK3) ),
inference(duplicate_literal_removal,[],[f78]) ).
tff(f81,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK0,X0)
| ~ '$ki_accessible'('$ki_local_world',sK0)
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_exists_in_world_$i'(X0,sK3) ),
inference(resolution,[],[f79,f32]) ).
tff(f82,plain,
! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_accessible'(sK0,X0) ),
inference(forward_subsumption_resolution,[],[f81,f31]) ).
tff(f83,plain,
( ~ '$ki_accessible'(sK2,sK4)
| ~ '$ki_accessible'(sK0,sK2) ),
inference(resolution,[],[f82,f34]) ).
tff(f84,plain,
~ '$ki_accessible'(sK0,sK2),
inference(forward_subsumption_resolution,[],[f83,f35]) ).
tff(f85,plain,
$false,
inference(forward_subsumption_resolution,[],[f84,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL953_8 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 17:03:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.54/1.18 % (2805146)Detected formulas, will run a generic FOF schedule.
% 2.54/1.18 % (2805247)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2700606248:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.54/1.18 % (2805247)First to succeed.
% 2.54/1.18 % (2805247)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2805146"
% 2.54/1.18 % (2805245)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=230962132:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.54/1.18 % (2805246)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=461381838:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.54/1.18 % (2805243)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=3520789412:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.54/1.18 % (2805244)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=153277357:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.54/1.18 % (2805246)Also succeeded, but the first one will report.
% 2.54/1.18 % (2805249)dis-21_1_sil=8000:lcm=predicate:random_seed=701959557: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)
% 2.54/1.18 % (2805248)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2664026434:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.54/1.18 % (2805249)Also succeeded, but the first one will report.
% 2.54/1.18 % (2805248)Also succeeded, but the first one will report.
% 2.54/1.18 % (2805247)Refutation found. Thanks to Tanya!
% 2.54/1.18 % SZS status Theorem for theBenchmark
% 2.54/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.29 % (2805247)------------------------------
% 2.73/1.29 % (2805247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.29 % (2805247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.29 % (2805247)CaDiCaL version: 2.1.3
% 2.73/1.29 % (2805247)Termination reason: Refutation
% 2.73/1.29 % (2805247)Time elapsed: 0.003 s
% 2.73/1.29 % (2805247)Peak memory usage: 88 MB
% 2.73/1.29 % (2805247)Instructions burned: 6 (million)
% 2.73/1.29 % (2805247)------------------------------
% 2.73/1.29 % (2805247)------------------------------
% 2.73/1.29 % (2805146)Success in time 0.319 s
% 2.73/1.29 % Vampire exiting
%------------------------------------------------------------------------------