TSTP Solution File: NLP266_23 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : NLP266_23 : 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_uns --cores 0 -t %d %s
% Computer : n003.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 15:39:54 EDT 2023
% Result : Theorem 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 32
% Syntax : Number of formulae : 78 ( 16 unt; 18 typ; 0 def)
% Number of atoms : 402 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 428 ( 152 ~; 136 |; 96 &)
% ( 0 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 66 ( 66 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 45 ( 15 >; 30 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 4 prp; 0-5 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-5 aty)
% Number of variables : 242 (; 193 !; 49 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_4,type,
sK2: '$ki_world' > $i ).
tff(func_def_5,type,
sK3: ( '$ki_world' * $i * $i * $i ) > $i ).
tff(func_def_6,type,
sK4: ( '$ki_world' * $i * $i * $i * $i ) > '$ki_world' ).
tff(func_def_7,type,
sK5: ( '$ki_world' * $i * $i * $i * $i ) > $i ).
tff(func_def_8,type,
sK6: '$ki_world' ).
tff(func_def_9,type,
sK7: ( $i * $i ) > '$ki_world' ).
tff(func_def_10,type,
sK8: '$ki_world' > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
number: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_3,type,
string: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
in: ( '$ki_world' * $i * $i * $i ) > $o ).
tff(pred_def_5,type,
do: ( '$ki_world' * $i * $i * $i ) > $o ).
tff(pred_def_6,type,
entry_box: ( '$ki_world' * $i ) > $o ).
tff(pred_def_7,type,
userid: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_8,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(pred_def_9,type,
sP0: ( '$ki_world' * $i * $i * $i * $i ) > $o ).
tff(f154,plain,
$false,
inference(unit_resulting_resolution,[],[f42,f70,f42,f54,f43,f65,f43,f54,f74,f75,f46]) ).
tff(f46,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( ~ do(X5,X1,sK3(X0,X1,X2,X3),X6)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_exists_in_world_$i'(X5,X6)
| ~ string(X0,X2)
| ~ entry_box(X0,X3)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X3)
| ~ '$ki_accessible'(X0,X5)
| in(X5,X2,X3,X6) ),
inference(cnf_transformation,[],[f29]) ).
tff(f29,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ! [X2] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| ! [X3] :
( ( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X0,X5)
| ! [X6] :
( ~ do(X5,X1,sK3(X0,X1,X2,X3),X6)
| in(X5,X2,X3,X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) ) )
& '$ki_exists_in_world_$i'(X0,sK3(X0,X1,X2,X3)) )
| ~ string(X0,X2)
| ~ entry_box(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X3) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f18,f28]) ).
tff(f28,plain,
! [X0: '$ki_world',X1,X2,X3] :
( ? [X4] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X0,X5)
| ! [X6] :
( ~ do(X5,X1,X4,X6)
| in(X5,X2,X3,X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) ) )
& '$ki_exists_in_world_$i'(X0,X4) )
=> ( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X0,X5)
| ! [X6] :
( ~ do(X5,X1,sK3(X0,X1,X2,X3),X6)
| in(X5,X2,X3,X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) ) )
& '$ki_exists_in_world_$i'(X0,sK3(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f18,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ! [X2] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| ! [X3] :
( ? [X4] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X0,X5)
| ! [X6] :
( ~ do(X5,X1,X4,X6)
| in(X5,X2,X3,X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) ) )
& '$ki_exists_in_world_$i'(X0,X4) )
| ~ string(X0,X2)
| ~ entry_box(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X3) ) ) ) ),
inference(flattening,[],[f17]) ).
tff(f17,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ? [X4] :
( ! [X5: '$ki_world'] :
( ! [X6] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,X4,X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'(X0,X5) )
& '$ki_exists_in_world_$i'(X0,X4) )
| ~ entry_box(X0,X3)
| ~ string(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X3) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$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] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ( ( entry_box(X0,X3)
& string(X0,X2) )
=> ? [X4] :
( ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ! [X6] :
( '$ki_exists_in_world_$i'(X5,X6)
=> ( do(X5,X1,X4,X6)
=> in(X5,X2,X3,X6) ) ) )
& '$ki_exists_in_world_$i'(X0,X4) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X6] :
( '$ki_exists_in_world_$i'(X0,X6)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ! [X5] :
( '$ki_exists_in_world_$i'(X0,X5)
=> ( ( string(X0,X3)
& entry_box(X0,X5) )
=> ? [X7] :
( ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ! [X8] :
( '$ki_exists_in_world_$i'(X4,X8)
=> ( do(X4,X6,X7,X8)
=> in(X4,X3,X5,X8) ) ) )
& '$ki_exists_in_world_$i'(X0,X7) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f75,plain,
! [X2: '$ki_world',X0: $i,X1: $i] : ~ in(sK4(sK6,X0,X1,sK1,sK8(X2)),sK8(X2),sK1,sK5(sK6,X0,X1,sK1,sK8(X2))),
inference(unit_resulting_resolution,[],[f73,f47]) ).
tff(f47,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X4: $i] :
( ~ in(sK4(X0,X1,X2,X3,X4),X4,X3,sK5(X0,X1,X2,X3,X4))
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: '$ki_world',X1,X2,X3,X4] :
( ( '$ki_accessible'(X0,sK4(X0,X1,X2,X3,X4))
& do(sK4(X0,X1,X2,X3,X4),X2,X1,sK5(X0,X1,X2,X3,X4))
& '$ki_exists_in_world_$i'(sK4(X0,X1,X2,X3,X4),sK5(X0,X1,X2,X3,X4))
& ~ in(sK4(X0,X1,X2,X3,X4),X4,X3,sK5(X0,X1,X2,X3,X4)) )
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f31,f33,f32]) ).
tff(f32,plain,
! [X0: '$ki_world',X1,X2,X3,X4] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
& ? [X6] :
( do(X5,X2,X1,X6)
& '$ki_exists_in_world_$i'(X5,X6)
& ~ in(X5,X4,X3,X6) ) )
=> ( '$ki_accessible'(X0,sK4(X0,X1,X2,X3,X4))
& ? [X6] :
( do(sK4(X0,X1,X2,X3,X4),X2,X1,X6)
& '$ki_exists_in_world_$i'(sK4(X0,X1,X2,X3,X4),X6)
& ~ in(sK4(X0,X1,X2,X3,X4),X4,X3,X6) ) ) ),
introduced(choice_axiom,[]) ).
tff(f33,plain,
! [X0: '$ki_world',X1,X2,X3,X4] :
( ? [X6] :
( do(sK4(X0,X1,X2,X3,X4),X2,X1,X6)
& '$ki_exists_in_world_$i'(sK4(X0,X1,X2,X3,X4),X6)
& ~ in(sK4(X0,X1,X2,X3,X4),X4,X3,X6) )
=> ( do(sK4(X0,X1,X2,X3,X4),X2,X1,sK5(X0,X1,X2,X3,X4))
& '$ki_exists_in_world_$i'(sK4(X0,X1,X2,X3,X4),sK5(X0,X1,X2,X3,X4))
& ~ in(sK4(X0,X1,X2,X3,X4),X4,X3,sK5(X0,X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f31,plain,
! [X0: '$ki_world',X1,X2,X3,X4] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
& ? [X6] :
( do(X5,X2,X1,X6)
& '$ki_exists_in_world_$i'(X5,X6)
& ~ in(X5,X4,X3,X6) ) )
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f30]) ).
tff(f30,plain,
! [X0: '$ki_world',X3,X4,X2,X1] :
( ? [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
& ? [X7] :
( do(X6,X4,X3,X7)
& '$ki_exists_in_world_$i'(X6,X7)
& ~ in(X6,X1,X2,X7) ) )
| ~ sP0(X0,X3,X4,X2,X1) ),
inference(nnf_transformation,[],[f21]) ).
tff(f21,plain,
! [X0: '$ki_world',X3,X4,X2,X1] :
( ? [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
& ? [X7] :
( do(X6,X4,X3,X7)
& '$ki_exists_in_world_$i'(X6,X7)
& ~ in(X6,X1,X2,X7) ) )
| ~ sP0(X0,X3,X4,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f73,plain,
! [X2: '$ki_world',X0: $i,X1: $i] : sP0(sK6,X0,X1,sK1,sK8(X2)),
inference(unit_resulting_resolution,[],[f65,f67,f63,f61]) ).
tff(f61,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ userid(sK7(X1,X2),u,X1)
| ~ number(sK7(X1,X2),X2,one)
| ~ entry_box(sK7(X1,X2),X2)
| sP0(sK6,X3,X4,X2,X1) ),
inference(subsumption_resolution,[],[f60,f54]) ).
tff(f60,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ '$ki_exists_in_world_$i'(sK6,X3)
| ~ userid(sK7(X1,X2),u,X1)
| ~ number(sK7(X1,X2),X2,one)
| sP0(sK6,X3,X4,X2,X1)
| ~ entry_box(sK7(X1,X2),X2) ),
inference(subsumption_resolution,[],[f59,f54]) ).
tff(f59,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ userid(sK7(X1,X2),u,X1)
| ~ number(sK7(X1,X2),X2,one)
| ~ '$ki_exists_in_world_$i'(sK6,X2)
| sP0(sK6,X3,X4,X2,X1)
| ~ '$ki_exists_in_world_$i'(sK6,X3)
| ~ entry_box(sK7(X1,X2),X2) ),
inference(subsumption_resolution,[],[f58,f54]) ).
tff(f58,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ '$ki_exists_in_world_$i'(sK6,X1)
| ~ entry_box(sK7(X1,X2),X2)
| ~ userid(sK7(X1,X2),u,X1)
| ~ number(sK7(X1,X2),X2,one)
| ~ '$ki_exists_in_world_$i'(sK6,X3)
| sP0(sK6,X3,X4,X2,X1)
| ~ '$ki_exists_in_world_$i'(sK6,X2) ),
inference(subsumption_resolution,[],[f53,f54]) ).
tff(f53,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ '$ki_exists_in_world_$i'(sK6,X4)
| sP0(sK6,X3,X4,X2,X1)
| ~ userid(sK7(X1,X2),u,X1)
| ~ number(sK7(X1,X2),X2,one)
| ~ '$ki_exists_in_world_$i'(sK6,X1)
| ~ '$ki_exists_in_world_$i'(sK6,X2)
| ~ entry_box(sK7(X1,X2),X2)
| ~ '$ki_exists_in_world_$i'(sK6,X3) ),
inference(cnf_transformation,[],[f37]) ).
tff(f37,plain,
( ! [X1] :
( ~ '$ki_exists_in_world_$i'(sK6,X1)
| ! [X2] :
( ! [X3] :
( ~ '$ki_exists_in_world_$i'(sK6,X3)
| ! [X4] :
( ( ( ~ entry_box(sK7(X1,X2),X2)
| ~ number(sK7(X1,X2),X2,one)
| ~ userid(sK7(X1,X2),u,X1) )
& '$ki_accessible'(sK6,sK7(X1,X2)) )
| ~ '$ki_exists_in_world_$i'(sK6,X4)
| sP0(sK6,X3,X4,X2,X1) ) )
| ~ '$ki_exists_in_world_$i'(sK6,X2) ) )
& '$ki_accessible'('$ki_local_world',sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f22,f36,f35]) ).
tff(f35,plain,
( ? [X0: '$ki_world'] :
( ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ! [X2] :
( ! [X3] :
( ~ '$ki_exists_in_world_$i'(X0,X3)
| ! [X4] :
( ? [X5: '$ki_world'] :
( ( ~ entry_box(X5,X2)
| ~ number(X5,X2,one)
| ~ userid(X5,u,X1) )
& '$ki_accessible'(X0,X5) )
| ~ '$ki_exists_in_world_$i'(X0,X4)
| sP0(X0,X3,X4,X2,X1) ) )
| ~ '$ki_exists_in_world_$i'(X0,X2) ) )
& '$ki_accessible'('$ki_local_world',X0) )
=> ( ! [X1] :
( ~ '$ki_exists_in_world_$i'(sK6,X1)
| ! [X2] :
( ! [X3] :
( ~ '$ki_exists_in_world_$i'(sK6,X3)
| ! [X4] :
( ? [X5: '$ki_world'] :
( ( ~ entry_box(X5,X2)
| ~ number(X5,X2,one)
| ~ userid(X5,u,X1) )
& '$ki_accessible'(sK6,X5) )
| ~ '$ki_exists_in_world_$i'(sK6,X4)
| sP0(sK6,X3,X4,X2,X1) ) )
| ~ '$ki_exists_in_world_$i'(sK6,X2) ) )
& '$ki_accessible'('$ki_local_world',sK6) ) ),
introduced(choice_axiom,[]) ).
tff(f36,plain,
! [X1,X2] :
( ? [X5: '$ki_world'] :
( ( ~ entry_box(X5,X2)
| ~ number(X5,X2,one)
| ~ userid(X5,u,X1) )
& '$ki_accessible'(sK6,X5) )
=> ( ( ~ entry_box(sK7(X1,X2),X2)
| ~ number(sK7(X1,X2),X2,one)
| ~ userid(sK7(X1,X2),u,X1) )
& '$ki_accessible'(sK6,sK7(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f22,plain,
? [X0: '$ki_world'] :
( ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ! [X2] :
( ! [X3] :
( ~ '$ki_exists_in_world_$i'(X0,X3)
| ! [X4] :
( ? [X5: '$ki_world'] :
( ( ~ entry_box(X5,X2)
| ~ number(X5,X2,one)
| ~ userid(X5,u,X1) )
& '$ki_accessible'(X0,X5) )
| ~ '$ki_exists_in_world_$i'(X0,X4)
| sP0(X0,X3,X4,X2,X1) ) )
| ~ '$ki_exists_in_world_$i'(X0,X2) ) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(definition_folding,[],[f20,f21]) ).
tff(f20,plain,
? [X0: '$ki_world'] :
( ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ! [X2] :
( ! [X3] :
( ~ '$ki_exists_in_world_$i'(X0,X3)
| ! [X4] :
( ? [X5: '$ki_world'] :
( ( ~ entry_box(X5,X2)
| ~ number(X5,X2,one)
| ~ userid(X5,u,X1) )
& '$ki_accessible'(X0,X5) )
| ~ '$ki_exists_in_world_$i'(X0,X4)
| ? [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
& ? [X7] :
( do(X6,X4,X3,X7)
& '$ki_exists_in_world_$i'(X6,X7)
& ~ in(X6,X1,X2,X7) ) ) ) )
| ~ '$ki_exists_in_world_$i'(X0,X2) ) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f19]) ).
tff(f19,plain,
? [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ '$ki_exists_in_world_$i'(X0,X4)
| ? [X5: '$ki_world'] :
( ( ~ entry_box(X5,X2)
| ~ number(X5,X2,one)
| ~ userid(X5,u,X1) )
& '$ki_accessible'(X0,X5) )
| ? [X6: '$ki_world'] :
( ? [X7] :
( ~ in(X6,X1,X2,X7)
& do(X6,X4,X3,X7)
& '$ki_exists_in_world_$i'(X6,X7) )
& '$ki_accessible'(X0,X6) ) )
| ~ '$ki_exists_in_world_$i'(X0,X3) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f9,plain,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( '$ki_exists_in_world_$i'(X0,X4)
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ( userid(X5,u,X1)
& entry_box(X5,X2)
& number(X5,X2,one) ) )
& ! [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
=> ! [X7] :
( '$ki_exists_in_world_$i'(X6,X7)
=> ( do(X6,X4,X3,X7)
=> in(X6,X1,X2,X7) ) ) ) )
& '$ki_exists_in_world_$i'(X0,X3) )
& '$ki_exists_in_world_$i'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) ) ),
inference(rectify,[],[f8]) ).
tff(f8,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
& ? [X5] :
( '$ki_exists_in_world_$i'(X0,X5)
& ? [X7] :
( '$ki_exists_in_world_$i'(X0,X7)
& ? [X6] :
( ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ( userid(X4,u,X3)
& entry_box(X4,X5)
& number(X4,X5,one) ) )
& ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ! [X8] :
( '$ki_exists_in_world_$i'(X4,X8)
=> ( do(X4,X6,X7,X8)
=> in(X4,X3,X5,X8) ) ) )
& '$ki_exists_in_world_$i'(X0,X6) ) ) ) ) ),
inference(negated_conjecture,[],[f7]) ).
tff(f7,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
& ? [X5] :
( '$ki_exists_in_world_$i'(X0,X5)
& ? [X7] :
( '$ki_exists_in_world_$i'(X0,X7)
& ? [X6] :
( ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ( userid(X4,u,X3)
& entry_box(X4,X5)
& number(X4,X5,one) ) )
& ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ! [X8] :
( '$ki_exists_in_world_$i'(X4,X8)
=> ( do(X4,X6,X7,X8)
=> in(X4,X3,X5,X8) ) ) )
& '$ki_exists_in_world_$i'(X0,X6) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f63,plain,
! [X2: '$ki_world',X0: '$ki_world'] : userid(X2,u,sK8(X0)),
inference(subsumption_resolution,[],[f62,f43]) ).
tff(f62,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ '$ki_accessible'(X0,X2)
| userid(X2,u,sK8(X0)) ),
inference(subsumption_resolution,[],[f56,f43]) ).
tff(f56,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| userid(X2,u,sK8(X0))
| ~ '$ki_accessible'(X0,X2) ),
inference(cnf_transformation,[],[f39]) ).
tff(f39,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X0,X2)
| ( string(X2,sK8(X0))
& userid(X2,u,sK8(X0)) ) )
& '$ki_exists_in_world_$i'(X0,sK8(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f16,f38]) ).
tff(f38,plain,
! [X0: '$ki_world'] :
( ? [X1] :
( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X0,X2)
| ( string(X2,X1)
& userid(X2,u,X1) ) )
& '$ki_exists_in_world_$i'(X0,X1) )
=> ( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X0,X2)
| ( string(X2,sK8(X0))
& userid(X2,u,sK8(X0)) ) )
& '$ki_exists_in_world_$i'(X0,sK8(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f16,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ? [X1] :
( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X0,X2)
| ( string(X2,X1)
& userid(X2,u,X1) ) )
& '$ki_exists_in_world_$i'(X0,X1) ) ),
inference(ennf_transformation,[],[f10]) ).
tff(f10,plain,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1] :
( ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ( string(X2,X1)
& userid(X2,u,X1) ) )
& '$ki_exists_in_world_$i'(X0,X1) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X3] :
( ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ( userid(X4,u,X3)
& string(X4,X3) ) )
& '$ki_exists_in_world_$i'(X0,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(f67,plain,
! [X0: '$ki_world'] : number(X0,sK1,one),
inference(unit_resulting_resolution,[],[f43,f40]) ).
tff(f40,plain,
! [X1: '$ki_world'] :
( number(X1,sK1,one)
| ~ '$ki_accessible'('$ki_local_world',X1) ),
inference(cnf_transformation,[],[f24]) ).
tff(f24,plain,
( '$ki_exists_in_world_$i'('$ki_local_world',sK1)
& ! [X1: '$ki_world'] :
( ( entry_box(X1,sK1)
& number(X1,sK1,one) )
| ~ '$ki_accessible'('$ki_local_world',X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f15,f23]) ).
tff(f23,plain,
( ? [X0] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( ( entry_box(X1,X0)
& number(X1,X0,one) )
| ~ '$ki_accessible'('$ki_local_world',X1) ) )
=> ( '$ki_exists_in_world_$i'('$ki_local_world',sK1)
& ! [X1: '$ki_world'] :
( ( entry_box(X1,sK1)
& number(X1,sK1,one) )
| ~ '$ki_accessible'('$ki_local_world',X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f15,plain,
? [X0] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( ( entry_box(X1,X0)
& number(X1,X0,one) )
| ~ '$ki_accessible'('$ki_local_world',X1) ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f11,plain,
? [X0] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( entry_box(X1,X0)
& number(X1,X0,one) ) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
? [X5] :
( '$ki_exists_in_world_$i'('$ki_local_world',X5)
& ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( number(X0,X5,one)
& entry_box(X0,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(f74,plain,
! [X2: '$ki_world',X0: $i,X1: $i] : do(sK4(sK6,X0,X1,sK1,sK8(X2)),X1,X0,sK5(sK6,X0,X1,sK1,sK8(X2))),
inference(unit_resulting_resolution,[],[f73,f49]) ).
tff(f49,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X4: $i] :
( do(sK4(X0,X1,X2,X3,X4),X2,X1,sK5(X0,X1,X2,X3,X4))
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f34]) ).
tff(f65,plain,
! [X0: '$ki_world'] : entry_box(X0,sK1),
inference(unit_resulting_resolution,[],[f43,f41]) ).
tff(f41,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| entry_box(X1,sK1) ),
inference(cnf_transformation,[],[f24]) ).
tff(f43,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X1,X0),
inference(cnf_transformation,[],[f25]) ).
tff(f25,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X1,X0),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X1: '$ki_world',X0: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
tff(f54,plain,
! [X0: $i,X1: '$ki_world'] : '$ki_exists_in_world_$i'(X1,X0),
inference(cnf_transformation,[],[f12]) ).
tff(f12,plain,
! [X0,X1: '$ki_world'] : '$ki_exists_in_world_$i'(X1,X0),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X2,X0: '$ki_world'] : '$ki_exists_in_world_$i'(X0,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f70,plain,
! [X0: '$ki_world'] : string(X0,sK8(sK6)),
inference(unit_resulting_resolution,[],[f43,f51,f57]) ).
tff(f57,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( string(X2,sK8(X0))
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f39]) ).
tff(f51,plain,
'$ki_accessible'('$ki_local_world',sK6),
inference(cnf_transformation,[],[f37]) ).
tff(f42,plain,
'$ki_exists_in_world_$i'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NLP266_23 : TPTP v8.2.0. Released v8.2.0.
% 0.04/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 22 12:10:48 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 % (15584)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.47 % (15593)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.48 % (15584)First to succeed.
% 0.19/0.48 % (15584)Refutation found. Thanks to Tanya!
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48 % (15584)------------------------------
% 0.19/0.48 % (15584)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48 % (15584)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48 % (15584)Termination reason: Refutation
% 0.19/0.48
% 0.19/0.48 % (15584)Memory used [KB]: 6012
% 0.19/0.48 % (15584)Time elapsed: 0.078 s
% 0.19/0.48 % (15584)Instructions burned: 5 (million)
% 0.19/0.48 % (15584)------------------------------
% 0.19/0.48 % (15584)------------------------------
% 0.19/0.48 % (15572)Success in time 0.128 s
%------------------------------------------------------------------------------