%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL947_10 : 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 : 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 12:01:13 PM UTC 2026
% Result : Theorem 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 17 unt; 0 typ; 3 def)
% Number of atoms : 320 ( 0 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 307 ( 130 ~; 137 |; 11 &)
% ( 3 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 74 ( 74 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 13 usr; 5 prp; 0-4 aty)
% Number of functors : 39 ( 39 usr; 3 con; 0-4 aty)
% Number of variables : 136 ( 0 sgn 130 !; 6 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_2,type,
sK3: '$ki_world' > $i ).
tff(func_def_3,type,
sK4: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_4,type,
sK5: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_5,type,
sK6: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_6,type,
sK7: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_7,type,
sK8: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_8,type,
sK9: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_9,type,
sK10: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_10,type,
sK11: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_11,type,
sK12: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_12,type,
sK13: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_13,type,
sK14: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_14,type,
sK15: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_15,type,
sK16: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_16,type,
sK17: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_17,type,
sK18: ( $i * $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_18,type,
sK19: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_19,type,
sK20: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_20,type,
sK21: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_21,type,
sK22: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_22,type,
sK23: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_23,type,
sK24: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_24,type,
sK25: ( $i * $i * '$ki_world' ) > $i ).
tff(func_def_25,type,
sK26: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_26,type,
sK27: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_27,type,
sK28: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_28,type,
sK29: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_29,type,
sK30: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_30,type,
sK31: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_31,type,
sK32: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_32,type,
sK33: ( $i * $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_33,type,
sK34: ( $i * $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_34,type,
sK35: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_35,type,
sK36: ( $i * $i * '$ki_world' ) > $i ).
tff(func_def_36,type,
sK37: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_37,type,
sK38: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_38,type,
sK39: '$ki_world' ).
tff(func_def_40,type,
sK41: '$ki_world' ).
tff(pred_def_1,type,
'$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(pred_def_6,type,
sP0: ( $i * $i * '$ki_world' ) > $o ).
tff(pred_def_7,type,
sP1: ( $i * $i * $i * '$ki_world' ) > $o ).
tff(pred_def_8,type,
sP2: ( $i * $i * '$ki_world' ) > $o ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f2,axiom,
! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
( ( '$ki_accessible'(X0,X1)
& '$ki_accessible'(X1,X2) )
=> '$ki_accessible'(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).
tff(f13,axiom,
! [X0: '$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'] :
( '$ki_accessible'(X4,X5)
=> qmltpeq(X5,union(X1,X3),X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_union) ).
tff(f18,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> subset(X2,X1,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
tff(f20,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> qmltpeq(X2,union(X1,X1),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f21,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> qmltpeq(X2,union(X1,X1),X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
tff(f30,plain,
! [X0: '$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'] :
( '$ki_accessible'(X4,X6)
=> qmltpeq(X6,union(X1,X3),X3) ) ) ) ) ) ) ),
inference(rectify,[],[f13]) ).
tff(f35,plain,
! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
tff(f36,plain,
! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(X1,X2) ),
inference(flattening,[],[f35]) ).
tff(f54,plain,
! [X0: '$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,[],[f30]) ).
tff(f55,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,[],[f54]) ).
tff(f63,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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f18]) ).
tff(f66,plain,
? [X0: '$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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f21]) ).
tff(f89,plain,
! [X0: '$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,[],[f55]) ).
tff(f90,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(sK17(X1,X3,X4),X1,X3)
& '$ki_accessible'(X4,sK17(X1,X3,X4)) )
| ~ '$ki_accessible'(X2,X4) )
| ~ '$ki_exists_in_world_$i'(X2,X3) )
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X6,sK17(X1,X3,X4))],[f89]) ).
tff(f108,plain,
( ~ qmltpeq(sK41,union(sK40,sK40),sK40)
& '$ki_accessible'(sK39,sK41)
& '$ki_exists_in_world_$i'(sK39,sK40)
& '$ki_accessible'('$ki_local_world',sK39) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39,sK40,sK41]),skolemize(X0,sK39),skolemize(X1,sK40),skolemize(X2,sK41)],[f66]) ).
tff(f109,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f110,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,[],[f36]) ).
tff(f139,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)
| '$ki_accessible'(X4,sK17(X1,X3,X4))
| ~ '$ki_accessible'(X2,X4)
| ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f90]) ).
tff(f140,plain,
! [X2: '$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)
| ~ subset(sK17(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,[],[f90]) ).
tff(f167,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,[],[f63]) ).
tff(f187,plain,
'$ki_accessible'('$ki_local_world',sK39),
inference(cnf_transformation,[],[f108]) ).
tff(f188,plain,
'$ki_exists_in_world_$i'(sK39,sK40),
inference(cnf_transformation,[],[f108]) ).
tff(f189,plain,
'$ki_accessible'(sK39,sK41),
inference(cnf_transformation,[],[f108]) ).
tff(f190,plain,
~ qmltpeq(sK41,union(sK40,sK40),sK40),
inference(cnf_transformation,[],[f108]) ).
tff(f191,plain,
! [X0: '$ki_world'] : ~ '$ki_accessible'(X0,X0),
inference(consistent_polarity_flipping,[],[f109]) ).
tff(f192,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( '$ki_accessible'(X1,X2)
| '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(X0,X2) ),
inference(consistent_polarity_flipping,[],[f110]) ).
tff(f220,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
| '$ki_accessible'(X4,X5)
| ~ subset(sK17(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)
| ~ qmltpeq(X5,union(X1,X3),X3) ),
inference(consistent_polarity_flipping,[],[f140]) ).
tff(f221,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
| '$ki_accessible'(X4,X5)
| ~ '$ki_accessible'(X4,sK17(X1,X3,X4))
| '$ki_accessible'(X2,X4)
| ~ '$ki_exists_in_world_$i'(X2,X3)
| '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ qmltpeq(X5,union(X1,X3),X3) ),
inference(consistent_polarity_flipping,[],[f139]) ).
tff(f248,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
( '$ki_accessible'('$ki_local_world',X0)
| '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| subset(X2,X1,X1) ),
inference(consistent_polarity_flipping,[],[f167]) ).
tff(f268,plain,
qmltpeq(sK41,union(sK40,sK40),sK40),
inference(consistent_polarity_flipping,[],[f190]) ).
tff(f269,plain,
~ '$ki_accessible'(sK39,sK41),
inference(consistent_polarity_flipping,[],[f189]) ).
tff(f270,plain,
~ '$ki_accessible'('$ki_local_world',sK39),
inference(consistent_polarity_flipping,[],[f187]) ).
tff(f285,plain,
! [X0: '$ki_world',X1: $i] :
( '$ki_accessible'(sK39,X0)
| ~ '$ki_exists_in_world_$i'(sK39,X1)
| subset(X0,X1,X1) ),
inference(resolution,[],[f248,f270]) ).
tff(f443,definition,
( spl42_2
<=> '$ki_exists_in_world_$i'(sK39,sK40) ),
introduced(definition,[new_symbols(definition,[spl42_2])],[avatar_definition]) ).
tff(f445,plain,
( ~ '$ki_exists_in_world_$i'(sK39,sK40)
| spl42_2 ),
inference(avatar_component_clause,[],[f443]) ).
tff(f451,plain,
( $false
| spl42_2 ),
inference(resolution,[],[f445,f188]) ).
tff(f452,plain,
spl42_2,
inference(avatar_contradiction_clause,[],[f451]) ).
tff(f672,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: '$ki_world',X4: '$ki_world'] :
( '$ki_accessible'(sK39,X4)
| ~ '$ki_accessible'(X0,sK17(X2,X3,X0))
| '$ki_accessible'(X4,X0)
| ~ '$ki_exists_in_world_$i'(X4,X3)
| '$ki_accessible'(X0,X1)
| ~ '$ki_exists_in_world_$i'(sK39,X2)
| ~ qmltpeq(X1,union(X2,X3),X3) ),
inference(resolution,[],[f221,f270]) ).
tff(f699,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: '$ki_world',X4: '$ki_world'] :
( '$ki_accessible'(sK39,X4)
| ~ subset(sK17(X2,X3,X0),X2,X3)
| '$ki_accessible'(X4,X0)
| ~ '$ki_exists_in_world_$i'(X4,X3)
| '$ki_accessible'(X0,X1)
| ~ '$ki_exists_in_world_$i'(sK39,X2)
| ~ qmltpeq(X1,union(X2,X3),X3) ),
inference(resolution,[],[f220,f270]) ).
tff(f1033,plain,
! [X2: $i,X3: '$ki_world',X0: '$ki_world',X1: $i] :
( '$ki_accessible'(sK39,X0)
| ~ '$ki_accessible'(X0,sK17(X1,X2,X0))
| ~ '$ki_exists_in_world_$i'(sK39,X2)
| '$ki_accessible'(X0,X3)
| ~ '$ki_exists_in_world_$i'(sK39,X1)
| ~ qmltpeq(X3,union(X1,X2),X2) ),
inference(resolution,[],[f672,f191]) ).
tff(f1044,definition,
( spl42_7
<=> '$ki_accessible'(sK41,sK17(sK40,sK40,sK41)) ),
introduced(definition,[new_symbols(definition,[spl42_7])],[avatar_definition]) ).
tff(f1046,plain,
( ~ '$ki_accessible'(sK41,sK17(sK40,sK40,sK41))
| spl42_7 ),
inference(avatar_component_clause,[],[f1044]) ).
tff(f1102,plain,
( ! [X0: '$ki_world'] :
( '$ki_accessible'(X0,sK41)
| ~ '$ki_accessible'(X0,sK17(sK40,sK40,sK41)) )
| spl42_7 ),
inference(resolution,[],[f1046,f192]) ).
tff(f1115,plain,
( ~ '$ki_accessible'(sK39,sK17(sK40,sK40,sK41))
| spl42_7 ),
inference(resolution,[],[f1102,f269]) ).
tff(f1154,plain,
( ! [X0: $i] :
( subset(sK17(sK40,sK40,sK41),X0,X0)
| ~ '$ki_exists_in_world_$i'(sK39,X0) )
| spl42_7 ),
inference(resolution,[],[f1115,f285]) ).
tff(f1326,plain,
! [X2: '$ki_world',X0: $i,X1: $i] :
( '$ki_accessible'(sK41,X2)
| ~ '$ki_exists_in_world_$i'(sK39,X1)
| ~ '$ki_accessible'(sK41,sK17(X0,X1,sK41))
| ~ '$ki_exists_in_world_$i'(sK39,X0)
| ~ qmltpeq(X2,union(X0,X1),X1) ),
inference(resolution,[],[f1033,f269]) ).
tff(f1333,plain,
! [X0: $i,X1: $i] :
( ~ qmltpeq(sK41,union(X1,X0),X0)
| ~ '$ki_accessible'(sK41,sK17(X1,X0,sK41))
| ~ '$ki_exists_in_world_$i'(sK39,X1)
| ~ '$ki_exists_in_world_$i'(sK39,X0) ),
inference(resolution,[],[f1326,f191]) ).
tff(f1334,plain,
( ~ '$ki_accessible'(sK41,sK17(sK40,sK40,sK41))
| ~ '$ki_exists_in_world_$i'(sK39,sK40)
| ~ '$ki_exists_in_world_$i'(sK39,sK40) ),
inference(resolution,[],[f1333,f268]) ).
tff(f1335,plain,
( ~ '$ki_accessible'(sK41,sK17(sK40,sK40,sK41))
| ~ '$ki_exists_in_world_$i'(sK39,sK40) ),
inference(duplicate_literal_removal,[],[f1334]) ).
tff(f1672,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: $i,X1: $i] :
( '$ki_accessible'(sK39,X2)
| ~ subset(sK17(X0,X1,X2),X0,X1)
| ~ '$ki_exists_in_world_$i'(sK39,X1)
| '$ki_accessible'(X2,X3)
| ~ '$ki_exists_in_world_$i'(sK39,X0)
| ~ qmltpeq(X3,union(X0,X1),X1) ),
inference(resolution,[],[f699,f191]) ).
tff(f1939,plain,
! [X2: '$ki_world',X0: $i,X1: $i] :
( '$ki_accessible'(sK41,X2)
| ~ '$ki_exists_in_world_$i'(sK39,X1)
| ~ subset(sK17(X0,X1,sK41),X0,X1)
| ~ '$ki_exists_in_world_$i'(sK39,X0)
| ~ qmltpeq(X2,union(X0,X1),X1) ),
inference(resolution,[],[f1672,f269]) ).
tff(f1947,plain,
! [X0: $i,X1: $i] :
( ~ subset(sK17(X1,X0,sK41),X1,X0)
| ~ '$ki_exists_in_world_$i'(sK39,X0)
| ~ '$ki_exists_in_world_$i'(sK39,X1)
| ~ qmltpeq(sK41,union(X1,X0),X0) ),
inference(resolution,[],[f1939,f191]) ).
tff(f1949,plain,
( ~ '$ki_exists_in_world_$i'(sK39,sK40)
| ~ '$ki_exists_in_world_$i'(sK39,sK40)
| ~ qmltpeq(sK41,union(sK40,sK40),sK40)
| ~ '$ki_exists_in_world_$i'(sK39,sK40)
| spl42_7 ),
inference(resolution,[],[f1947,f1154]) ).
tff(f2078,plain,
( ~ '$ki_exists_in_world_$i'(sK39,sK40)
| ~ qmltpeq(sK41,union(sK40,sK40),sK40)
| spl42_7 ),
inference(duplicate_literal_removal,[],[f1949]) ).
tff(f2085,definition,
( spl42_10
<=> qmltpeq(sK41,union(sK40,sK40),sK40) ),
introduced(definition,[new_symbols(definition,[spl42_10])],[avatar_definition]) ).
tff(f2087,plain,
( ~ qmltpeq(sK41,union(sK40,sK40),sK40)
| spl42_10 ),
inference(avatar_component_clause,[],[f2085]) ).
tff(f2195,plain,
( ~ spl42_10
| ~ spl42_2
| spl42_7 ),
inference(avatar_split_clause,[],[f2078,f1044,f443,f2085]) ).
tff(f2405,plain,
( $false
| spl42_10 ),
inference(resolution,[],[f2087,f268]) ).
tff(f2406,plain,
spl42_10,
inference(avatar_contradiction_clause,[],[f2405]) ).
tff(f2407,plain,
( ~ spl42_2
| ~ spl42_7 ),
inference(avatar_split_clause,[],[f1335,f1044,f443]) ).
cnf(s2,plain,
spl42_2,
inference(sat_conversion,[],[f452]) ).
cnf(s45,plain,
( ~ spl42_2
| spl42_7
| ~ spl42_10 ),
inference(sat_conversion,[],[f2195]) ).
cnf(s47,plain,
spl42_10,
inference(sat_conversion,[],[f2406]) ).
cnf(s48,plain,
( ~ spl42_2
| ~ spl42_7 ),
inference(sat_conversion,[],[f2407]) ).
cnf(s50,plain,
( ~ spl42_2
| spl42_7 ),
inference(rat,[],[s45,s47]) ).
cnf(s90,plain,
~ spl42_7,
inference(rat,[],[s48,s2]) ).
cnf(s91,plain,
$false,
inference(rat,[],[s50,s90,s2]) ).
tff(f2408,plain,
$false,
inference(avatar_sat_refutation,[],[s91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL947_10 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 17:10:23 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 Running first-order model finding
% 0.12/0.39 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
% 0.15/0.48 % (2599858)Will run a generic schedule for satisfiability detection.
% 0.15/0.48 % (2599873)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4107629835:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.48 % (2599867)% WARNING: option uhcvi not known.
% 0.15/0.48 % (2599868)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=129587141:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.48 % (2599871)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=877139383:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.48 % (2599866)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=193918631_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.48 % (2599867)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=417304076:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.48 % (2599872)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1626649579:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.48 % (2599870)dis+10_1_sil=32000:sp=arity:random_seed=3274114319:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.48 % TRYING [1]
% 0.15/0.48 % TRYING [2]
% 0.15/0.48 % (2599872) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2599858-2599872"...
% 0.15/0.48 % (2599873) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2599858-2599873"...
% 0.15/0.48 % (2599873)...printing done.
% 0.15/0.48 % (2599872)...printing done.
% 0.15/0.48 % (2599873)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Theorem for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.49 % (2599873)------------------------------
% 0.15/0.49 % (2599873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.49 % (2599873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.49 % (2599873)CaDiCaL version: 2.1.3
% 0.15/0.49 % (2599873)Termination reason: Refutation
% 0.15/0.49 % (2599873)Time elapsed: 0.045 s
% 0.15/0.49 % (2599873)Peak memory usage: 14 MB
% 0.15/0.49 % (2599873)Instructions burned: 144 (million)
% 0.15/0.49 % (2599858)Success in time 0.082 s
% 0.15/0.49 % Vampire exiting
%------------------------------------------------------------------------------