%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL947_10 : 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 : n018.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 11:57:16 AM UTC 2026
% Result : Theorem 2.74s 1.27s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 317 ( 0 equ)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 391 ( 186 ~; 168 |; 11 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 69 ( 69 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 136 ( 130 !; 6 ?; 136 :)
% 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_5,type,
sK3: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_6,type,
sK4: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_7,type,
sK5: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_8,type,
sK6: ( $i * $i * '$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' ) > '$ki_world' ).
tff(func_def_11,type,
sK9: '$ki_world' > $i ).
tff(func_def_12,type,
sK10: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_13,type,
sK11: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_14,type,
sK12: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_15,type,
sK13: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_16,type,
sK14: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_17,type,
sK15: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_18,type,
sK16: ( $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 ) > $o ).
tff(pred_def_3,type,
member: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_4,type,
subset: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_5,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f2,axiom,
! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
( ( '$ki_accessible'(X0,X1)
& '$ki_accessible'(X1,X2) )
=> '$ki_accessible'(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
tff(f13,axiom,
! [X0: '$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'] :
( '$ki_accessible'(X4,X5)
=> subset(X5,X1,X3) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> qmltpeq(X5,union(X1,X3),X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_union) ).
tff(f18,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> subset(X2,X1,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
tff(f20,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> qmltpeq(X2,union(X1,X1),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f21,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> qmltpeq(X2,union(X1,X1),X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
tff(f22,plain,
! [X0: '$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'] :
( '$ki_accessible'(X4,X5)
=> subset(X5,X1,X3) )
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X4,X6)
=> qmltpeq(X6,union(X1,X3),X3) ) ) ) ) ) ) ),
inference(rectify,[],[f13]) ).
tff(f30,plain,
? [X0: '$ki_world'] :
( ? [X1: $i] :
( ? [X2: '$ki_world'] :
( ~ qmltpeq(X2,union(X1,X1),X1)
& '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f21]) ).
tff(f31,plain,
! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
tff(f32,plain,
! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(X1,X2) ),
inference(flattening,[],[f31]) ).
tff(f34,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ! [X4: '$ki_world'] :
( ! [X6: '$ki_world'] :
( qmltpeq(X6,union(X1,X3),X3)
| ~ '$ki_accessible'(X4,X6) )
| ? [X5: '$ki_world'] :
( ~ subset(X5,X1,X3)
& '$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,[],[f22]) ).
tff(f35,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ! [X4: '$ki_world'] :
( ! [X6: '$ki_world'] :
( qmltpeq(X6,union(X1,X3),X3)
| ~ '$ki_accessible'(X4,X6) )
| ? [X5: '$ki_world'] :
( ~ subset(X5,X1,X3)
& '$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,[],[f34]) ).
tff(f45,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( subset(X2,X1,X1)
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f18]) ).
tff(f52,plain,
( ~ qmltpeq(sK2,union(sK1,sK1),sK1)
& '$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]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f30]) ).
tff(f53,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( qmltpeq(X5,union(X1,X3),X3)
| ~ '$ki_accessible'(X4,X5) )
| ? [X6: '$ki_world'] :
( ~ subset(X6,X1,X3)
& '$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,[],[f35]) ).
tff(f54,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: '$ki_world'] :
( ! [X3: $i] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( qmltpeq(X5,union(X1,X3),X3)
| ~ '$ki_accessible'(X4,X5) )
| ( ~ subset(sK3(X1,X3,X4),X1,X3)
& '$ki_accessible'(X4,sK3(X1,X3,X4)) )
| ~ '$ki_accessible'(X2,X4) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X6,sK3(X1,X3,X4))],[f53]) ).
tff(f70,plain,
'$ki_accessible'('$ki_local_world',sK0),
inference(cnf_transformation,[],[f52]) ).
tff(f71,plain,
'$ki_exists_in_world_$i'(sK0,sK1),
inference(cnf_transformation,[],[f52]) ).
tff(f72,plain,
'$ki_accessible'(sK0,sK2),
inference(cnf_transformation,[],[f52]) ).
tff(f73,plain,
~ qmltpeq(sK2,union(sK1,sK1),sK1),
inference(cnf_transformation,[],[f52]) ).
tff(f74,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
tff(f75,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f77,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( qmltpeq(X5,union(X1,X3),X3)
| ~ '$ki_accessible'(X4,X5)
| '$ki_accessible'(X4,sK3(X1,X3,X4))
| ~ '$ki_accessible'(X2,X4)
| ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f54]) ).
tff(f78,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( ~ subset(sK3(X1,X3,X4),X1,X3)
| ~ '$ki_accessible'(X4,X5)
| qmltpeq(X5,union(X1,X3),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,[],[f54]) ).
tff(f91,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
( subset(X2,X1,X1)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f45]) ).
tff(f114,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( '$ki_accessible'(X0,sK3(sK1,sK1,X0))
| ~ '$ki_accessible'(X0,sK2)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'(X2,X1)
| ~ '$ki_exists_in_world_$i'(X2,sK1)
| ~ '$ki_accessible'('$ki_local_world',X2) ),
inference(resolution,[],[f77,f73]) ).
tff(f118,plain,
! [X2: $i,X3: '$ki_world',X0: '$ki_world',X1: '$ki_world',X4: '$ki_world',X5: '$ki_world'] :
( qmltpeq(X1,union(X2,X2),X2)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(X3,X0)
| ~ '$ki_exists_in_world_$i'(X3,X2)
| ~ '$ki_accessible'(X4,X3)
| ~ '$ki_exists_in_world_$i'(X4,X2)
| ~ '$ki_accessible'('$ki_local_world',X4)
| ~ '$ki_accessible'(X5,sK3(X2,X2,X0))
| ~ '$ki_exists_in_world_$i'(X5,X2)
| ~ '$ki_accessible'('$ki_local_world',X5) ),
inference(resolution,[],[f78,f91]) ).
tff(f163,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(X3,sK3(sK1,sK1,X0))
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'(X2,X1)
| ~ '$ki_exists_in_world_$i'(X2,sK1)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(X0,sK2)
| ~ '$ki_exists_in_world_$i'(X3,sK1)
| ~ '$ki_accessible'('$ki_local_world',X3) ),
inference(resolution,[],[f118,f73]) ).
tff(f167,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world',X4: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X2,X0)
| ~ '$ki_exists_in_world_$i'(X2,sK1)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(X1,sK2)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,sK2)
| ~ '$ki_accessible'(X3,X1)
| ~ '$ki_exists_in_world_$i'(X3,sK1)
| ~ '$ki_accessible'(X4,X3)
| ~ '$ki_exists_in_world_$i'(X4,sK1)
| ~ '$ki_accessible'('$ki_local_world',X4) ),
inference(resolution,[],[f163,f114]) ).
tff(f173,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world',X4: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X4,sK1)
| ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X2,X0)
| ~ '$ki_exists_in_world_$i'(X2,sK1)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(X1,sK2)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X3,X1)
| ~ '$ki_exists_in_world_$i'(X3,sK1)
| ~ '$ki_accessible'(X4,X3)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X4) ),
inference(duplicate_literal_removal,[],[f167]) ).
tff(f225,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X2,sK2)
| ~ '$ki_exists_in_world_$i'(X2,sK1)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(X3,X2)
| ~ '$ki_exists_in_world_$i'(X3,sK1)
| ~ '$ki_accessible'(X0,X3)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(factoring,[],[f173]) ).
tff(f232,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X2,sK2)
| ~ '$ki_exists_in_world_$i'(X2,sK1)
| ~ '$ki_accessible'(X3,X2)
| ~ '$ki_exists_in_world_$i'(X3,sK1)
| ~ '$ki_accessible'(X0,X3)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f225,f74]) ).
tff(f235,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X2,sK2)
| ~ '$ki_exists_in_world_$i'(X2,sK1)
| ~ '$ki_accessible'(X3,X2)
| ~ '$ki_exists_in_world_$i'(X3,sK1)
| ~ '$ki_accessible'(X0,X3)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f232,f74]) ).
tff(f236,plain,
! [X2: '$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)
| ~ '$ki_accessible'(X2,sK2)
| ~ '$ki_exists_in_world_$i'(X2,sK1)
| ~ '$ki_accessible'(X3,X2)
| ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X0,X3) ),
inference(forward_subsumption_resolution,[],[f235,f74]) ).
tff(f248,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X2,sK2)
| ~ '$ki_exists_in_world_$i'(X2,sK1)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'(X0,X0) ),
inference(factoring,[],[f236]) ).
tff(f249,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X2,sK1)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X2,sK2)
| ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X0,X2) ),
inference(forward_subsumption_resolution,[],[f248,f75]) ).
tff(f253,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X0,sK2)
| ~ '$ki_accessible'(X0,X0) ),
inference(factoring,[],[f249]) ).
tff(f254,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f253,f75]) ).
tff(f265,plain,
! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X0,X0)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK2) ),
inference(factoring,[],[f254]) ).
tff(f266,plain,
! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f265,f75]) ).
tff(f269,plain,
( ~ '$ki_accessible'('$ki_local_world',sK0)
| ~ '$ki_accessible'(sK0,sK2) ),
inference(resolution,[],[f266,f71]) ).
tff(f270,plain,
~ '$ki_accessible'(sK0,sK2),
inference(forward_subsumption_resolution,[],[f269,f70]) ).
tff(f271,plain,
$false,
inference(forward_subsumption_resolution,[],[f270,f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL947_10 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n018.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 17:10:24 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.74/1.27 % (2600102)Detected formulas, will run a generic FOF schedule.
% 2.74/1.27 % (2600145)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=2476163678:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.74/1.27 % (2600147)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=4042369958:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.74/1.27 % (2600146)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=2787888215:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.74/1.27 % (2600150)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2693045188:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.74/1.27 % (2600149)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3514754425:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.74/1.27 % (2600148)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1076415208:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.74/1.27 % (2600151)dis-21_1_sil=8000:lcm=predicate:random_seed=3574434048: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)
% 2.74/1.27 % (2600148)Refutation not found, incomplete strategy
% 2.74/1.27 % (2600148)------------------------------
% 2.74/1.27 % (2600148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.27 % (2600148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.27 % (2600148)CaDiCaL version: 2.1.3
% 2.74/1.27 % (2600148)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.27 % (2600148)Time elapsed: 0.008 s
% 2.74/1.27 % (2600148)Peak memory usage: 88 MB
% 2.74/1.27 % (2600148)Instructions burned: 13 (million)
% 2.74/1.27 % (2600149)First to succeed.
% 2.74/1.27 % (2600150)Also succeeded, but the first one will report.
% 2.74/1.27 % (2600149)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2600102"
% 2.74/1.27 % (2600151)Instruction limit reached!
% 2.74/1.27 % (2600151)------------------------------
% 2.74/1.27 % (2600151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.27 % (2600151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.27 % (2600151)CaDiCaL version: 2.1.3
% 2.74/1.27 % (2600151)Termination reason: Instruction limit
% 2.74/1.27 % (2600151)Termination phase: Saturation
% 2.74/1.27 % (2600151)Time elapsed: 0.059 s
% 2.74/1.27 % (2600151)Peak memory usage: 88 MB
% 2.74/1.27 % (2600151)Instructions burned: 130 (million)
% 2.74/1.27 % (2600159)lrs+10_1_sil=8000:sp=occurrence:random_seed=1391400287:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.74/1.27 % (2600148)------------------------------
% 2.74/1.27 % (2600148)------------------------------
% 2.74/1.27 % (2600149)Refutation found. Thanks to Tanya!
% 2.74/1.27 % SZS status Theorem for theBenchmark
% 2.74/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.45/1.36 % (2600149)------------------------------
% 3.45/1.36 % (2600149)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.36 % (2600149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.36 % (2600149)CaDiCaL version: 2.1.3
% 3.45/1.36 % (2600149)Termination reason: Refutation
% 3.45/1.36 % (2600149)Time elapsed: 0.012 s
% 3.45/1.36 % (2600149)Peak memory usage: 88 MB
% 3.45/1.36 % (2600149)Instructions burned: 19 (million)
% 3.45/1.36 % (2600149)------------------------------
% 3.45/1.36 % (2600149)------------------------------
% 3.45/1.36 % (2600102)Success in time 0.415 s
% 3.45/1.36 % Vampire exiting
%------------------------------------------------------------------------------