TSTP Solution File: LCL953_8 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : LCL953_8 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n022.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 : Mon May 22 15:38:44 EDT 2023
% Result : Theorem 0.21s 0.53s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 33
% Syntax : Number of formulae : 83 ( 10 unt; 18 typ; 0 def)
% Number of atoms : 509 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 513 ( 201 ~; 160 |; 94 &)
% ( 5 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 132 ( 132 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 27 ( 12 >; 15 *; 0 +; 0 <<)
% Number of predicates : 14 ( 13 usr; 8 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 199 (; 134 !; 65 ?; 165 :)
% 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: '$ki_world' > '$ki_world' ).
tff(func_def_8,type,
sK6: '$ki_world' ).
tff(func_def_9,type,
sK7: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_10,type,
sK8: '$ki_world' > $i ).
tff(func_def_11,type,
sK9: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_14,type,
sK12: '$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' ) > '$ki_world' ).
tff(pred_def_1,type,
'$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(f381,plain,
$false,
inference(avatar_sat_refutation,[],[f82,f86,f368,f373,f377,f380]) ).
tff(f380,plain,
( spl15_2
| ~ spl15_51 ),
inference(avatar_split_clause,[],[f379,f366,f80]) ).
tff(f80,plain,
( spl15_2
<=> ! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X0,sK2)
| ~ '$ki_accessible'('$ki_local_world',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
tff(f366,plain,
( spl15_51
<=> ! [X0: '$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_exists_in_world_$i'(X1,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_51])]) ).
tff(f379,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'(X0,sK2)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'(X0,sK1) )
| ~ spl15_51 ),
inference(subsumption_resolution,[],[f378,f52]) ).
tff(f52,plain,
'$ki_accessible'(sK2,sK4),
inference(cnf_transformation,[],[f33]) ).
tff(f33,plain,
( '$ki_exists_in_world_$i'(sK2,sK3)
& ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(sK4,X5)
| ( ~ in(sK5(X5),sK1,sK3)
& '$ki_accessible'(X5,sK5(X5)) ) )
& ~ disjoint(sK6,singleton(sK1),sK3)
& '$ki_accessible'(sK4,sK6)
& '$ki_accessible'(sK2,sK4)
& '$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])],[f21,f32,f31,f30,f29,f28,f27,f26]) ).
tff(f26,plain,
( ? [X0: '$ki_world'] :
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( '$ki_exists_in_world_$i'(X2,X3)
& ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| ? [X6: '$ki_world'] :
( ~ in(X6,X1,X3)
& '$ki_accessible'(X5,X6) ) )
& ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(X1),X3)
& '$ki_accessible'(X4,X7) )
& '$ki_accessible'(X2,X4) ) )
& '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) )
=> ( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( '$ki_exists_in_world_$i'(X2,X3)
& ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| ? [X6: '$ki_world'] :
( ~ in(X6,X1,X3)
& '$ki_accessible'(X5,X6) ) )
& ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(X1),X3)
& '$ki_accessible'(X4,X7) )
& '$ki_accessible'(X2,X4) ) )
& '$ki_accessible'(sK0,X2) )
& '$ki_exists_in_world_$i'(sK0,X1) )
& '$ki_accessible'('$ki_local_world',sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f27,plain,
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( '$ki_exists_in_world_$i'(X2,X3)
& ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| ? [X6: '$ki_world'] :
( ~ in(X6,X1,X3)
& '$ki_accessible'(X5,X6) ) )
& ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(X1),X3)
& '$ki_accessible'(X4,X7) )
& '$ki_accessible'(X2,X4) ) )
& '$ki_accessible'(sK0,X2) )
& '$ki_exists_in_world_$i'(sK0,X1) )
=> ( ? [X2: '$ki_world'] :
( ? [X3] :
( '$ki_exists_in_world_$i'(X2,X3)
& ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| ? [X6: '$ki_world'] :
( ~ in(X6,sK1,X3)
& '$ki_accessible'(X5,X6) ) )
& ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(sK1),X3)
& '$ki_accessible'(X4,X7) )
& '$ki_accessible'(X2,X4) ) )
& '$ki_accessible'(sK0,X2) )
& '$ki_exists_in_world_$i'(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f28,plain,
( ? [X2: '$ki_world'] :
( ? [X3] :
( '$ki_exists_in_world_$i'(X2,X3)
& ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| ? [X6: '$ki_world'] :
( ~ in(X6,sK1,X3)
& '$ki_accessible'(X5,X6) ) )
& ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(sK1),X3)
& '$ki_accessible'(X4,X7) )
& '$ki_accessible'(X2,X4) ) )
& '$ki_accessible'(sK0,X2) )
=> ( ? [X3] :
( '$ki_exists_in_world_$i'(sK2,X3)
& ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| ? [X6: '$ki_world'] :
( ~ in(X6,sK1,X3)
& '$ki_accessible'(X5,X6) ) )
& ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(sK1),X3)
& '$ki_accessible'(X4,X7) )
& '$ki_accessible'(sK2,X4) ) )
& '$ki_accessible'(sK0,sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f29,plain,
( ? [X3] :
( '$ki_exists_in_world_$i'(sK2,X3)
& ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| ? [X6: '$ki_world'] :
( ~ in(X6,sK1,X3)
& '$ki_accessible'(X5,X6) ) )
& ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(sK1),X3)
& '$ki_accessible'(X4,X7) )
& '$ki_accessible'(sK2,X4) ) )
=> ( '$ki_exists_in_world_$i'(sK2,sK3)
& ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| ? [X6: '$ki_world'] :
( ~ in(X6,sK1,sK3)
& '$ki_accessible'(X5,X6) ) )
& ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(sK1),sK3)
& '$ki_accessible'(X4,X7) )
& '$ki_accessible'(sK2,X4) ) ) ),
introduced(choice_axiom,[]) ).
tff(f30,plain,
( ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| ? [X6: '$ki_world'] :
( ~ in(X6,sK1,sK3)
& '$ki_accessible'(X5,X6) ) )
& ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(sK1),sK3)
& '$ki_accessible'(X4,X7) )
& '$ki_accessible'(sK2,X4) )
=> ( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(sK4,X5)
| ? [X6: '$ki_world'] :
( ~ in(X6,sK1,sK3)
& '$ki_accessible'(X5,X6) ) )
& ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(sK1),sK3)
& '$ki_accessible'(sK4,X7) )
& '$ki_accessible'(sK2,sK4) ) ),
introduced(choice_axiom,[]) ).
tff(f31,plain,
! [X5: '$ki_world'] :
( ? [X6: '$ki_world'] :
( ~ in(X6,sK1,sK3)
& '$ki_accessible'(X5,X6) )
=> ( ~ in(sK5(X5),sK1,sK3)
& '$ki_accessible'(X5,sK5(X5)) ) ),
introduced(choice_axiom,[]) ).
tff(f32,plain,
( ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(sK1),sK3)
& '$ki_accessible'(sK4,X7) )
=> ( ~ disjoint(sK6,singleton(sK1),sK3)
& '$ki_accessible'(sK4,sK6) ) ),
introduced(choice_axiom,[]) ).
tff(f21,plain,
? [X0: '$ki_world'] :
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( '$ki_exists_in_world_$i'(X2,X3)
& ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| ? [X6: '$ki_world'] :
( ~ in(X6,X1,X3)
& '$ki_accessible'(X5,X6) ) )
& ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(X1),X3)
& '$ki_accessible'(X4,X7) )
& '$ki_accessible'(X2,X4) ) )
& '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f20]) ).
tff(f20,plain,
? [X0: '$ki_world'] :
( ? [X1] :
( ? [X2: '$ki_world'] :
( ? [X3] :
( ? [X4: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ~ disjoint(X7,singleton(X1),X3)
& '$ki_accessible'(X4,X7) )
& ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| ? [X6: '$ki_world'] :
( ~ in(X6,X1,X3)
& '$ki_accessible'(X5,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(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'] :
( '$ki_accessible'(X5,X6)
=> disjoint(X6,singleton(X2),X4) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f378,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK2,sK4)
| ~ '$ki_accessible'(X0,sK2)
| ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'('$ki_local_world',X0) )
| ~ spl15_51 ),
inference(resolution,[],[f367,f57]) ).
tff(f57,plain,
'$ki_exists_in_world_$i'(sK2,sK3),
inference(cnf_transformation,[],[f33]) ).
tff(f367,plain,
( ! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X1,sK3)
| ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X1,sK4)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,X1) )
| ~ spl15_51 ),
inference(avatar_component_clause,[],[f366]) ).
tff(f377,plain,
~ spl15_50,
inference(avatar_contradiction_clause,[],[f376]) ).
tff(f376,plain,
( $false
| ~ spl15_50 ),
inference(subsumption_resolution,[],[f374,f53]) ).
tff(f53,plain,
'$ki_accessible'(sK4,sK6),
inference(cnf_transformation,[],[f33]) ).
tff(f374,plain,
( ~ '$ki_accessible'(sK4,sK6)
| ~ spl15_50 ),
inference(resolution,[],[f364,f54]) ).
tff(f54,plain,
~ disjoint(sK6,singleton(sK1),sK3),
inference(cnf_transformation,[],[f33]) ).
tff(f364,plain,
( ! [X2: '$ki_world'] :
( disjoint(X2,singleton(sK1),sK3)
| ~ '$ki_accessible'(sK4,X2) )
| ~ spl15_50 ),
inference(avatar_component_clause,[],[f363]) ).
tff(f363,plain,
( spl15_50
<=> ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(sK4,X2)
| disjoint(X2,singleton(sK1),sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_50])]) ).
tff(f373,plain,
( ~ spl15_1
| ~ spl15_49 ),
inference(avatar_contradiction_clause,[],[f372]) ).
tff(f372,plain,
( $false
| ~ spl15_1
| ~ spl15_49 ),
inference(subsumption_resolution,[],[f371,f52]) ).
tff(f371,plain,
( ~ '$ki_accessible'(sK2,sK4)
| ~ spl15_1
| ~ spl15_49 ),
inference(subsumption_resolution,[],[f370,f53]) ).
tff(f370,plain,
( ~ '$ki_accessible'(sK4,sK6)
| ~ '$ki_accessible'(sK2,sK4)
| ~ spl15_1
| ~ spl15_49 ),
inference(resolution,[],[f369,f78]) ).
tff(f78,plain,
( ! [X1: '$ki_world'] :
( '$ki_accessible'(X1,sK7(sK1,sK3,X1))
| ~ '$ki_accessible'(X1,sK6)
| ~ '$ki_accessible'(sK2,X1) )
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f77]) ).
tff(f77,plain,
( spl15_1
<=> ! [X1: '$ki_world'] :
( '$ki_accessible'(X1,sK7(sK1,sK3,X1))
| ~ '$ki_accessible'(X1,sK6)
| ~ '$ki_accessible'(sK2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
tff(f369,plain,
( ~ '$ki_accessible'(sK4,sK7(sK1,sK3,sK4))
| ~ spl15_49 ),
inference(resolution,[],[f361,f56]) ).
tff(f56,plain,
! [X5: '$ki_world'] :
( ~ in(sK5(X5),sK1,sK3)
| ~ '$ki_accessible'(sK4,X5) ),
inference(cnf_transformation,[],[f33]) ).
tff(f361,plain,
( in(sK5(sK7(sK1,sK3,sK4)),sK1,sK3)
| ~ spl15_49 ),
inference(avatar_component_clause,[],[f359]) ).
tff(f359,plain,
( spl15_49
<=> in(sK5(sK7(sK1,sK3,sK4)),sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_49])]) ).
tff(f368,plain,
( spl15_49
| spl15_50
| spl15_51
| ~ spl15_1 ),
inference(avatar_split_clause,[],[f357,f77,f366,f363,f359]) ).
tff(f357,plain,
( ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X1,sK4)
| ~ '$ki_accessible'(sK4,X2)
| ~ '$ki_exists_in_world_$i'(X1,sK3)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,X1)
| in(sK5(sK7(sK1,sK3,sK4)),sK1,sK3)
| disjoint(X2,singleton(sK1),sK3) )
| ~ spl15_1 ),
inference(subsumption_resolution,[],[f356,f53]) ).
tff(f356,plain,
( ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(sK4,sK6)
| in(sK5(sK7(sK1,sK3,sK4)),sK1,sK3)
| ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(sK4,X2)
| ~ '$ki_exists_in_world_$i'(X1,sK3)
| ~ '$ki_accessible'(X1,sK4)
| ~ '$ki_accessible'('$ki_local_world',X0)
| disjoint(X2,singleton(sK1),sK3)
| ~ '$ki_accessible'(X0,X1) )
| ~ spl15_1 ),
inference(subsumption_resolution,[],[f355,f52]) ).
tff(f355,plain,
( ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X1,sK4)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(sK2,sK4)
| ~ '$ki_accessible'(sK4,sK6)
| ~ '$ki_accessible'(sK4,X2)
| disjoint(X2,singleton(sK1),sK3)
| in(sK5(sK7(sK1,sK3,sK4)),sK1,sK3)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'(X1,sK3) )
| ~ spl15_1 ),
inference(resolution,[],[f319,f78]) ).
tff(f319,plain,
! [X10: '$ki_world',X11: '$ki_world',X8: '$ki_world',X6: '$ki_world',X9: $i,X7: $i] :
( ~ '$ki_accessible'(sK4,sK7(X9,X7,X11))
| ~ '$ki_exists_in_world_$i'(X10,X9)
| in(sK5(sK7(X9,X7,X11)),X9,X7)
| ~ '$ki_accessible'(X10,X6)
| ~ '$ki_accessible'(X6,X11)
| disjoint(X8,singleton(X9),X7)
| ~ '$ki_accessible'(X11,X8)
| ~ '$ki_accessible'('$ki_local_world',X10)
| ~ '$ki_exists_in_world_$i'(X6,X7) ),
inference(resolution,[],[f59,f55]) ).
tff(f55,plain,
! [X5: '$ki_world'] :
( '$ki_accessible'(X5,sK5(X5))
| ~ '$ki_accessible'(sK4,X5) ),
inference(cnf_transformation,[],[f33]) ).
tff(f59,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_exists_in_world_$i'(X2,X3)
| disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'('$ki_local_world',X0)
| in(X7,X1,X3)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'(X2,X4)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'(X4,X5) ),
inference(cnf_transformation,[],[f36]) ).
tff(f36,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X0,X2)
| ! [X3] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X2,X4)
| ( ! [X7: '$ki_world'] :
( ~ '$ki_accessible'(sK7(X1,X3,X4),X7)
| in(X7,X1,X3) )
& '$ki_accessible'(X4,sK7(X1,X3,X4)) ) )
| ~ '$ki_exists_in_world_$i'(X2,X3) ) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f34,f35]) ).
tff(f35,plain,
! [X1,X3,X4: '$ki_world'] :
( ? [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( ~ '$ki_accessible'(X6,X7)
| in(X7,X1,X3) )
& '$ki_accessible'(X4,X6) )
=> ( ! [X7: '$ki_world'] :
( ~ '$ki_accessible'(sK7(X1,X3,X4),X7)
| in(X7,X1,X3) )
& '$ki_accessible'(X4,sK7(X1,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f34,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X0,X2)
| ! [X3] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( disjoint(X5,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X2,X4)
| ? [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( ~ '$ki_accessible'(X6,X7)
| in(X7,X1,X3) )
& '$ki_accessible'(X4,X6) ) )
| ~ '$ki_exists_in_world_$i'(X2,X3) ) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(rectify,[],[f23]) ).
tff(f23,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X0,X2)
| ! [X3] :
( ! [X4: '$ki_world'] :
( ! [X7: '$ki_world'] :
( disjoint(X7,singleton(X1),X3)
| ~ '$ki_accessible'(X4,X7) )
| ~ '$ki_accessible'(X2,X4)
| ? [X5: '$ki_world'] :
( ! [X6: '$ki_world'] :
( ~ '$ki_accessible'(X5,X6)
| in(X6,X1,X3) )
& '$ki_accessible'(X4,X5) ) )
| ~ '$ki_exists_in_world_$i'(X2,X3) ) ) )
| ~ '$ki_accessible'('$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: '$ki_world'] :
( ~ '$ki_accessible'(X5,X6)
| in(X6,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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f14]) ).
tff(f14,plain,
! [X0: '$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(f86,plain,
~ spl15_2,
inference(avatar_contradiction_clause,[],[f85]) ).
tff(f85,plain,
( $false
| ~ spl15_2 ),
inference(subsumption_resolution,[],[f84,f49]) ).
tff(f49,plain,
'$ki_accessible'('$ki_local_world',sK0),
inference(cnf_transformation,[],[f33]) ).
tff(f84,plain,
( ~ '$ki_accessible'('$ki_local_world',sK0)
| ~ spl15_2 ),
inference(subsumption_resolution,[],[f83,f51]) ).
tff(f51,plain,
'$ki_accessible'(sK0,sK2),
inference(cnf_transformation,[],[f33]) ).
tff(f83,plain,
( ~ '$ki_accessible'(sK0,sK2)
| ~ '$ki_accessible'('$ki_local_world',sK0)
| ~ spl15_2 ),
inference(resolution,[],[f81,f50]) ).
tff(f50,plain,
'$ki_exists_in_world_$i'(sK0,sK1),
inference(cnf_transformation,[],[f33]) ).
tff(f81,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'(X0,sK2)
| ~ '$ki_accessible'('$ki_local_world',X0) )
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f80]) ).
tff(f82,plain,
( spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f75,f80,f77]) ).
tff(f75,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK1)
| '$ki_accessible'(X1,sK7(sK1,sK3,X1))
| ~ '$ki_accessible'(sK2,X1)
| ~ '$ki_accessible'(X1,sK6)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK2) ),
inference(resolution,[],[f74,f57]) ).
tff(f74,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X2,sK3)
| ~ '$ki_exists_in_world_$i'(X1,sK1)
| ~ '$ki_accessible'(X1,X2)
| ~ '$ki_accessible'(X2,X0)
| '$ki_accessible'(X0,sK7(sK1,sK3,X0))
| ~ '$ki_accessible'(X0,sK6)
| ~ '$ki_accessible'('$ki_local_world',X1) ),
inference(resolution,[],[f58,f54]) ).
tff(f58,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)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ '$ki_accessible'(X2,X4)
| '$ki_accessible'(X4,sK7(X1,X3,X4))
| ~ '$ki_exists_in_world_$i'(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL953_8 : TPTP v8.2.0. Released v8.2.0.
% 0.10/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 22 12:00:30 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.50 % (32451)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.50 % (32465)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.21/0.51 % (32444)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51 % (32455)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.51 % (32454)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.21/0.51 % (32448)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.51 % (32446)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.21/0.51 % (32471)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.21/0.51 % (32462)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.21/0.51 % (32445)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.52 % (32443)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.52 % (32447)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.52 % (32470)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.21/0.52 TRYING [1]
% 0.21/0.52 TRYING [2]
% 0.21/0.52 % (32448)Instruction limit reached!
% 0.21/0.52 % (32448)------------------------------
% 0.21/0.52 % (32448)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (32448)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52 % (32448)Termination reason: Unknown
% 0.21/0.52 % (32448)Termination phase: Saturation
% 0.21/0.52
% 0.21/0.52 % (32448)Memory used [KB]: 5628
% 0.21/0.52 % (32448)Time elapsed: 0.073 s
% 0.21/0.52 % (32448)Instructions burned: 8 (million)
% 0.21/0.52 % (32448)------------------------------
% 0.21/0.52 % (32448)------------------------------
% 0.21/0.52 % (32462)First to succeed.
% 0.21/0.53 % (32463)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.53 % (32461)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.53 % (32464)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.21/0.53 % (32453)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.53 % (32442)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.53 % (32462)Refutation found. Thanks to Tanya!
% 0.21/0.53 % SZS status Theorem for theBenchmark
% 0.21/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53 % (32462)------------------------------
% 0.21/0.53 % (32462)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53 % (32462)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53 % (32462)Termination reason: Refutation
% 0.21/0.53
% 0.21/0.53 % (32462)Memory used [KB]: 5756
% 0.21/0.53 % (32462)Time elapsed: 0.124 s
% 0.21/0.53 % (32462)Instructions burned: 9 (million)
% 0.21/0.53 % (32462)------------------------------
% 0.21/0.53 % (32462)------------------------------
% 0.21/0.53 % (32438)Success in time 0.175 s
%------------------------------------------------------------------------------