TSTP Solution File: LCL953_8 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL953_8 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:37:03 EDT 2024
% Result : Theorem 0.18s 0.35s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 59
% Syntax : Number of formulae : 130 ( 13 unt; 35 typ; 0 def)
% Number of atoms : 570 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 564 ( 217 ~; 178 |; 102 &)
% ( 14 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 128 ( 128 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 70 ( 29 >; 41 *; 0 +; 0 <<)
% Number of predicates : 35 ( 34 usr; 12 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 254 ( 182 !; 72 ?; 200 :)
% 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' > $i ).
tff(func_def_16,type,
sK14: '$ki_world' > '$ki_world' ).
tff(pred_def_1,type,
'$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 ) > $o ).
tff(pred_def_6,type,
sP15: ( '$ki_world' * $i ) > $o ).
tff(pred_def_7,type,
sP16: ( $i * '$ki_world' * $i ) > $o ).
tff(pred_def_8,type,
sP17: ( '$ki_world' * $i ) > $o ).
tff(pred_def_9,type,
sP18: ( $i * '$ki_world' * $i ) > $o ).
tff(pred_def_10,type,
sP19: ( '$ki_world' * $i ) > $o ).
tff(pred_def_11,type,
sP20: ( $i * '$ki_world' * $i ) > $o ).
tff(pred_def_12,type,
sP21: ( '$ki_world' * $i ) > $o ).
tff(pred_def_13,type,
sP22: ( $i * '$ki_world' * $i ) > $o ).
tff(pred_def_14,type,
sP23: ( '$ki_world' * $i ) > $o ).
tff(pred_def_15,type,
sP24: ( $i * '$ki_world' * $i ) > $o ).
tff(pred_def_16,type,
sP25: ( '$ki_world' * $i ) > $o ).
tff(pred_def_17,type,
sP26: ( $i * '$ki_world' * $i ) > $o ).
tff(pred_def_18,type,
sP27: ( '$ki_world' * $i ) > $o ).
tff(pred_def_19,type,
sP28: ( $i * '$ki_world' * $i ) > $o ).
tff(pred_def_20,type,
sP29: ( $i * '$ki_world' * $i ) > $o ).
tff(pred_def_21,type,
sP30: ( '$ki_world' * $i ) > $o ).
tff(pred_def_22,type,
sP31: ( $i * '$ki_world' * $i ) > $o ).
tff(f229,plain,
$false,
inference(avatar_sat_refutation,[],[f131,f159,f163,f179,f191,f193,f195,f205,f207,f228]) ).
tff(f228,plain,
( ~ spl32_4
| spl32_5
| spl32_9 ),
inference(avatar_split_clause,[],[f211,f202,f157,f153]) ).
tff(f153,plain,
( spl32_4
<=> '$ki_accessible'('$ki_local_world',sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_4])]) ).
tff(f157,plain,
( spl32_5
<=> ! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_accessible'(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_5])]) ).
tff(f202,plain,
( spl32_9
<=> sP28(sK3,sK4,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_9])]) ).
tff(f211,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(sK0,X0)
| ~ '$ki_accessible'('$ki_local_world',sK0)
| ~ '$ki_accessible'(X0,sK4) )
| spl32_9 ),
inference(resolution,[],[f209,f53]) ).
tff(f53,plain,
'$ki_exists_in_world_$i'(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
tff(f34,plain,
( ~ disjoint(sK5,singleton(sK1),sK3)
& '$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'('$ki_local_world',sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f26,f33,f32,f31,f30,f29,f28,f27]) ).
tff(f27,plain,
( ? [X0: '$ki_world'] :
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$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) )
=> ( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$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'(sK0,X2) )
& '$ki_exists_in_world_$i'(sK0,X1) )
& '$ki_accessible'('$ki_local_world',sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f28,plain,
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$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'(sK0,X2) )
& '$ki_exists_in_world_$i'(sK0,X1) )
=> ( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ disjoint(X5,singleton(sK1),X3)
& '$ki_accessible'(X4,X5) )
& ! [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ in(X7,sK1,X3)
& '$ki_accessible'(X6,X7) )
| ~ '$ki_accessible'(X4,X6) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(sK0,X2) )
& '$ki_exists_in_world_$i'(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f29,plain,
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ disjoint(X5,singleton(sK1),X3)
& '$ki_accessible'(X4,X5) )
& ! [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ in(X7,sK1,X3)
& '$ki_accessible'(X6,X7) )
| ~ '$ki_accessible'(X4,X6) )
& '$ki_accessible'(X2,X4) )
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'(sK0,X2) )
=> ( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ disjoint(X5,singleton(sK1),X3)
& '$ki_accessible'(X4,X5) )
& ! [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ in(X7,sK1,X3)
& '$ki_accessible'(X6,X7) )
| ~ '$ki_accessible'(X4,X6) )
& '$ki_accessible'(sK2,X4) )
& '$ki_exists_in_world_$i'(sK2,X3) )
& '$ki_accessible'(sK0,sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f30,plain,
( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ disjoint(X5,singleton(sK1),X3)
& '$ki_accessible'(X4,X5) )
& ! [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ in(X7,sK1,X3)
& '$ki_accessible'(X6,X7) )
| ~ '$ki_accessible'(X4,X6) )
& '$ki_accessible'(sK2,X4) )
& '$ki_exists_in_world_$i'(sK2,X3) )
=> ( ? [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ disjoint(X5,singleton(sK1),sK3)
& '$ki_accessible'(X4,X5) )
& ! [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ in(X7,sK1,sK3)
& '$ki_accessible'(X6,X7) )
| ~ '$ki_accessible'(X4,X6) )
& '$ki_accessible'(sK2,X4) )
& '$ki_exists_in_world_$i'(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
tff(f31,plain,
( ? [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ disjoint(X5,singleton(sK1),sK3)
& '$ki_accessible'(X4,X5) )
& ! [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ in(X7,sK1,sK3)
& '$ki_accessible'(X6,X7) )
| ~ '$ki_accessible'(X4,X6) )
& '$ki_accessible'(sK2,X4) )
=> ( ? [X5: '$ki_world'] :
( ~ disjoint(X5,singleton(sK1),sK3)
& '$ki_accessible'(sK4,X5) )
& ! [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ in(X7,sK1,sK3)
& '$ki_accessible'(X6,X7) )
| ~ '$ki_accessible'(sK4,X6) )
& '$ki_accessible'(sK2,sK4) ) ),
introduced(choice_axiom,[]) ).
tff(f32,plain,
( ? [X5: '$ki_world'] :
( ~ disjoint(X5,singleton(sK1),sK3)
& '$ki_accessible'(sK4,X5) )
=> ( ~ disjoint(sK5,singleton(sK1),sK3)
& '$ki_accessible'(sK4,sK5) ) ),
introduced(choice_axiom,[]) ).
tff(f33,plain,
! [X6: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ in(X7,sK1,sK3)
& '$ki_accessible'(X6,X7) )
=> ( ~ in(sK6(X6),sK1,sK3)
& '$ki_accessible'(X6,sK6(X6)) ) ),
introduced(choice_axiom,[]) ).
tff(f26,plain,
? [X0: '$ki_world'] :
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$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(f17,plain,
? [X0: '$ki_world'] :
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [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'('$ki_local_world',X0) ),
inference(flattening,[],[f16]) ).
tff(f16,plain,
? [X0: '$ki_world'] :
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$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(f10,plain,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ! [X3] :
( '$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'] :
( '$ki_accessible'(X4,X7)
=> disjoint(X7,singleton(X1),X3) ) ) ) ) ) ) ),
inference(rectify,[],[f9]) ).
tff(f9,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ! [X3: '$ki_world'] :
( '$ki_accessible'(X0,X3)
=> ! [X4] :
( '$ki_exists_in_world_$i'(X3,X4)
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
=> ( ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> ~ ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> in(X7,X2,X4) ) )
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> disjoint(X6,singleton(X2),X4) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f8]) ).
tff(f8,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ! [X3: '$ki_world'] :
( '$ki_accessible'(X0,X3)
=> ! [X4] :
( '$ki_exists_in_world_$i'(X3,X4)
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
=> ( ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> ~ ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> in(X7,X2,X4) ) )
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> disjoint(X6,singleton(X2),X4) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f209,plain,
( ! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X0,sK4) )
| spl32_9 ),
inference(resolution,[],[f208,f100]) ).
tff(f100,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
( sP27(X2,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,X2) ),
inference(cnf_transformation,[],[f100_D]) ).
tff(f100_D,plain,
! [X1,X2] :
( ! [X0] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,X2) )
<=> ~ sP27(X2,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP27])]) ).
tff(f208,plain,
( ! [X0: '$ki_world'] :
( ~ sP27(X0,sK1)
| ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(X0,sK4) )
| spl32_9 ),
inference(resolution,[],[f204,f102]) ).
tff(f102,plain,
! [X2: '$ki_world',X3: $i,X1: $i,X4: '$ki_world'] :
( sP28(X3,X4,X1)
| ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ sP27(X2,X1)
| ~ '$ki_accessible'(X2,X4) ),
inference(cnf_transformation,[],[f102_D]) ).
tff(f102_D,plain,
! [X1,X4,X3] :
( ! [X2] :
( ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ sP27(X2,X1)
| ~ '$ki_accessible'(X2,X4) )
<=> ~ sP28(X3,X4,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP28])]) ).
tff(f204,plain,
( ~ sP28(sK3,sK4,sK1)
| spl32_9 ),
inference(avatar_component_clause,[],[f202]) ).
tff(f207,plain,
spl32_8,
inference(avatar_contradiction_clause,[],[f206]) ).
tff(f206,plain,
( $false
| spl32_8 ),
inference(resolution,[],[f200,f59]) ).
tff(f59,plain,
'$ki_accessible'(sK4,sK5),
inference(cnf_transformation,[],[f34]) ).
tff(f200,plain,
( ~ '$ki_accessible'(sK4,sK5)
| spl32_8 ),
inference(avatar_component_clause,[],[f198]) ).
tff(f198,plain,
( spl32_8
<=> '$ki_accessible'(sK4,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_8])]) ).
tff(f205,plain,
( ~ spl32_8
| ~ spl32_9
| ~ spl32_1 ),
inference(avatar_split_clause,[],[f196,f121,f202,f198]) ).
tff(f121,plain,
( spl32_1
<=> sP29(sK3,sK4,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_1])]) ).
tff(f196,plain,
( ~ sP28(sK3,sK4,sK1)
| ~ '$ki_accessible'(sK4,sK5)
| ~ spl32_1 ),
inference(resolution,[],[f123,f113]) ).
tff(f113,plain,
! [X0: '$ki_world'] :
( ~ sP29(sK3,X0,sK1)
| ~ sP28(sK3,X0,sK1)
| ~ '$ki_accessible'(X0,sK5) ),
inference(resolution,[],[f105,f60]) ).
tff(f60,plain,
~ disjoint(sK5,singleton(sK1),sK3),
inference(cnf_transformation,[],[f34]) ).
tff(f105,plain,
! [X3: $i,X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X5)
| ~ sP28(X3,X4,X1)
| ~ sP29(X3,X4,X1) ),
inference(general_splitting,[],[f103,f104_D]) ).
tff(f104,plain,
! [X3: $i,X1: $i,X7: '$ki_world',X4: '$ki_world'] :
( ~ '$ki_accessible'(sK10(X1,X3,X4),X7)
| in(X7,X1,X3)
| sP29(X3,X4,X1) ),
inference(cnf_transformation,[],[f104_D]) ).
tff(f104_D,plain,
! [X1,X4,X3] :
( ! [X7] :
( ~ '$ki_accessible'(sK10(X1,X3,X4),X7)
| in(X7,X1,X3) )
<=> ~ sP29(X3,X4,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP29])]) ).
tff(f103,plain,
! [X3: $i,X1: $i,X7: '$ki_world',X4: '$ki_world',X5: '$ki_world'] :
( disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X5)
| in(X7,X1,X3)
| ~ '$ki_accessible'(sK10(X1,X3,X4),X7)
| ~ sP28(X3,X4,X1) ),
inference(general_splitting,[],[f101,f102_D]) ).
tff(f101,plain,
! [X2: '$ki_world',X3: $i,X1: $i,X7: '$ki_world',X4: '$ki_world',X5: '$ki_world'] :
( disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X5)
| in(X7,X1,X3)
| ~ '$ki_accessible'(sK10(X1,X3,X4),X7)
| ~ '$ki_accessible'(X2,X4)
| ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ sP27(X2,X1) ),
inference(general_splitting,[],[f69,f100_D]) ).
tff(f69,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X7: '$ki_world',X4: '$ki_world',X5: '$ki_world'] :
( disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X5)
| in(X7,X1,X3)
| ~ '$ki_accessible'(sK10(X1,X3,X4),X7)
| ~ '$ki_accessible'(X2,X4)
| ~ '$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,[],[f44]) ).
tff(f44,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2: '$ki_world'] :
( ! [X3] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X5) )
| ( ! [X7: '$ki_world'] :
( in(X7,X1,X3)
| ~ '$ki_accessible'(sK10(X1,X3,X4),X7) )
& '$ki_accessible'(X4,sK10(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(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f42,f43]) ).
tff(f43,plain,
! [X1,X3,X4: '$ki_world'] :
( ? [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( in(X7,X1,X3)
| ~ '$ki_accessible'(X6,X7) )
& '$ki_accessible'(X4,X6) )
=> ( ! [X7: '$ki_world'] :
( in(X7,X1,X3)
| ~ '$ki_accessible'(sK10(X1,X3,X4),X7) )
& '$ki_accessible'(X4,sK10(X1,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f42,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2: '$ki_world'] :
( ! [X3] :
( ! [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'('$ki_local_world',X0) ),
inference(rectify,[],[f23]) ).
tff(f23,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2: '$ki_world'] :
( ! [X3] :
( ! [X4: '$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,[],[f22]) ).
tff(f22,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2: '$ki_world'] :
( ! [X3] :
( ! [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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f13]) ).
tff(f13,plain,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ! [X3] :
( '$ki_exists_in_world_$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(f7,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ! [X3: '$ki_world'] :
( '$ki_accessible'(X0,X3)
=> ! [X4] :
( '$ki_exists_in_world_$i'(X3,X4)
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
=> ( ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> ~ ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> in(X7,X2,X4) ) )
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> disjoint(X6,singleton(X2),X4) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
tff(f123,plain,
( sP29(sK3,sK4,sK1)
| ~ spl32_1 ),
inference(avatar_component_clause,[],[f121]) ).
tff(f195,plain,
spl32_7,
inference(avatar_contradiction_clause,[],[f194]) ).
tff(f194,plain,
( $false
| spl32_7 ),
inference(resolution,[],[f190,f56]) ).
tff(f56,plain,
'$ki_accessible'(sK2,sK4),
inference(cnf_transformation,[],[f34]) ).
tff(f190,plain,
( ~ '$ki_accessible'(sK2,sK4)
| spl32_7 ),
inference(avatar_component_clause,[],[f188]) ).
tff(f188,plain,
( spl32_7
<=> '$ki_accessible'(sK2,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_7])]) ).
tff(f193,plain,
spl32_6,
inference(avatar_contradiction_clause,[],[f192]) ).
tff(f192,plain,
( $false
| spl32_6 ),
inference(resolution,[],[f186,f54]) ).
tff(f54,plain,
'$ki_accessible'(sK0,sK2),
inference(cnf_transformation,[],[f34]) ).
tff(f186,plain,
( ~ '$ki_accessible'(sK0,sK2)
| spl32_6 ),
inference(avatar_component_clause,[],[f184]) ).
tff(f184,plain,
( spl32_6
<=> '$ki_accessible'(sK0,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_6])]) ).
tff(f191,plain,
( ~ spl32_6
| ~ spl32_7
| ~ spl32_5 ),
inference(avatar_split_clause,[],[f182,f157,f188,f184]) ).
tff(f182,plain,
( ~ '$ki_accessible'(sK2,sK4)
| ~ '$ki_accessible'(sK0,sK2)
| ~ spl32_5 ),
inference(resolution,[],[f158,f55]) ).
tff(f55,plain,
'$ki_exists_in_world_$i'(sK2,sK3),
inference(cnf_transformation,[],[f34]) ).
tff(f158,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_accessible'(sK0,X0) )
| ~ spl32_5 ),
inference(avatar_component_clause,[],[f157]) ).
tff(f179,plain,
~ spl32_3,
inference(avatar_contradiction_clause,[],[f178]) ).
tff(f178,plain,
( $false
| ~ spl32_3 ),
inference(resolution,[],[f176,f59]) ).
tff(f176,plain,
( ~ '$ki_accessible'(sK4,sK5)
| ~ spl32_3 ),
inference(resolution,[],[f130,f60]) ).
tff(f130,plain,
( ! [X0: '$ki_world'] :
( disjoint(X0,singleton(sK1),sK3)
| ~ '$ki_accessible'(sK4,X0) )
| ~ spl32_3 ),
inference(avatar_component_clause,[],[f129]) ).
tff(f129,plain,
( spl32_3
<=> ! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK4,X0)
| disjoint(X0,singleton(sK1),sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_3])]) ).
tff(f163,plain,
spl32_4,
inference(avatar_contradiction_clause,[],[f162]) ).
tff(f162,plain,
( $false
| spl32_4 ),
inference(resolution,[],[f155,f52]) ).
tff(f52,plain,
'$ki_accessible'('$ki_local_world',sK0),
inference(cnf_transformation,[],[f34]) ).
tff(f155,plain,
( ~ '$ki_accessible'('$ki_local_world',sK0)
| spl32_4 ),
inference(avatar_component_clause,[],[f153]) ).
tff(f159,plain,
( ~ spl32_4
| spl32_5
| spl32_2 ),
inference(avatar_split_clause,[],[f136,f125,f157,f153]) ).
tff(f125,plain,
( spl32_2
<=> sP31(sK3,sK4,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_2])]) ).
tff(f136,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(sK0,X0)
| ~ '$ki_accessible'('$ki_local_world',sK0)
| ~ '$ki_accessible'(X0,sK4) )
| spl32_2 ),
inference(resolution,[],[f134,f53]) ).
tff(f134,plain,
( ! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X0,sK4) )
| spl32_2 ),
inference(resolution,[],[f132,f106]) ).
tff(f106,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
( sP30(X2,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,X2) ),
inference(cnf_transformation,[],[f106_D]) ).
tff(f106_D,plain,
! [X1,X2] :
( ! [X0] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,X2) )
<=> ~ sP30(X2,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP30])]) ).
tff(f132,plain,
( ! [X0: '$ki_world'] :
( ~ sP30(X0,sK1)
| ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(X0,sK4) )
| spl32_2 ),
inference(resolution,[],[f127,f108]) ).
tff(f108,plain,
! [X2: '$ki_world',X3: $i,X1: $i,X4: '$ki_world'] :
( sP31(X3,X4,X1)
| ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ sP30(X2,X1)
| ~ '$ki_accessible'(X2,X4) ),
inference(cnf_transformation,[],[f108_D]) ).
tff(f108_D,plain,
! [X1,X4,X3] :
( ! [X2] :
( ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ sP30(X2,X1)
| ~ '$ki_accessible'(X2,X4) )
<=> ~ sP31(X3,X4,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP31])]) ).
tff(f127,plain,
( ~ sP31(sK3,sK4,sK1)
| spl32_2 ),
inference(avatar_component_clause,[],[f125]) ).
tff(f131,plain,
( spl32_1
| ~ spl32_2
| spl32_3 ),
inference(avatar_split_clause,[],[f119,f129,f125,f121]) ).
tff(f119,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK4,X0)
| disjoint(X0,singleton(sK1),sK3)
| ~ sP31(sK3,sK4,sK1)
| sP29(sK3,sK4,sK1) ),
inference(resolution,[],[f109,f116]) ).
tff(f116,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK4,sK10(sK1,sK3,X0))
| sP29(sK3,X0,sK1) ),
inference(duplicate_literal_removal,[],[f115]) ).
tff(f115,plain,
! [X0: '$ki_world'] :
( sP29(sK3,X0,sK1)
| ~ '$ki_accessible'(sK4,sK10(sK1,sK3,X0))
| ~ '$ki_accessible'(sK4,sK10(sK1,sK3,X0)) ),
inference(resolution,[],[f111,f58]) ).
tff(f58,plain,
! [X6: '$ki_world'] :
( ~ in(sK6(X6),sK1,sK3)
| ~ '$ki_accessible'(sK4,X6) ),
inference(cnf_transformation,[],[f34]) ).
tff(f111,plain,
! [X2: '$ki_world',X0: $i,X1: $i] :
( in(sK6(sK10(X0,X1,X2)),X0,X1)
| sP29(X1,X2,X0)
| ~ '$ki_accessible'(sK4,sK10(X0,X1,X2)) ),
inference(resolution,[],[f104,f57]) ).
tff(f57,plain,
! [X6: '$ki_world'] :
( '$ki_accessible'(X6,sK6(X6))
| ~ '$ki_accessible'(sK4,X6) ),
inference(cnf_transformation,[],[f34]) ).
tff(f109,plain,
! [X3: $i,X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( '$ki_accessible'(X4,sK10(X1,X3,X4))
| ~ '$ki_accessible'(X4,X5)
| disjoint(X5,singleton(X1),X3)
| ~ sP31(X3,X4,X1) ),
inference(general_splitting,[],[f107,f108_D]) ).
tff(f107,plain,
! [X2: '$ki_world',X3: $i,X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X5)
| '$ki_accessible'(X4,sK10(X1,X3,X4))
| ~ '$ki_accessible'(X2,X4)
| ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ sP30(X2,X1) ),
inference(general_splitting,[],[f68,f106_D]) ).
tff(f68,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X5)
| '$ki_accessible'(X4,sK10(X1,X3,X4))
| ~ '$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,[],[f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL953_8 : TPTP v8.2.0. Released v8.2.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.32 % Computer : n006.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon May 20 02:13:08 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.18/0.33 % (29989)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.34 % (29992)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.18/0.34 % (29990)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.18/0.34 % (29994)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.18/0.34 % (29993)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.18/0.34 % (29992)First to succeed.
% 0.18/0.34 % (29996)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.18/0.34 % (29995)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.18/0.35 % (29991)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.18/0.35 TRYING [1,1]
% 0.18/0.35 % (29992)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-29989"
% 0.18/0.35 TRYING [2,1]
% 0.18/0.35 TRYING [1,1]
% 0.18/0.35 TRYING [2,1]
% 0.18/0.35 % (29992)Refutation found. Thanks to Tanya!
% 0.18/0.35 % SZS status Theorem for theBenchmark
% 0.18/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.35 % (29992)------------------------------
% 0.18/0.35 % (29992)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.35 % (29992)Termination reason: Refutation
% 0.18/0.35
% 0.18/0.35 % (29992)Memory used [KB]: 994
% 0.18/0.35 % (29992)Time elapsed: 0.008 s
% 0.18/0.35 % (29992)Instructions burned: 14 (million)
% 0.18/0.35 % (29989)Success in time 0.007 s
%------------------------------------------------------------------------------