TSTP Solution File: NLP266_4 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NLP266_4 : 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 01:05:45 EDT 2024
% Result : Theorem 0.16s 0.38s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 37
% Syntax : Number of formulae : 117 ( 17 unt; 20 typ; 0 def)
% Number of atoms : 539 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 557 ( 209 ~; 209 |; 94 &)
% ( 0 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 94 ( 94 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 50 ( 17 >; 33 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 4 prp; 0-5 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-5 aty)
% Number of variables : 337 ( 289 !; 48 ?; 214 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_3,type,
sK3: ( $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_4,type,
sK4: ( $i * $i * '$ki_world' * $i * $i ) > $i ).
tff(func_def_5,type,
sK5: '$ki_world' ).
tff(func_def_6,type,
sK6: ( $i * $i * $i * $i ) > '$ki_world' ).
tff(func_def_7,type,
sK7: ( '$ki_world' * $i * $i * $i ) > $i ).
tff(func_def_8,type,
sK8: '$ki_world' > $i ).
tff(func_def_9,type,
sK9: '$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: ( $i * $i * '$ki_world' * $i * $i ) > $o ).
tff(pred_def_10,type,
sP1: ( $i * $i * '$ki_world' ) > $o ).
tff(pred_def_11,type,
sP2: ( $i * '$ki_world' ) > $o ).
tff(f226,plain,
$false,
inference(subsumption_resolution,[],[f225,f145]) ).
tff(f145,plain,
number(sK3(sK10,sK8(sK5),sK5),sK10,one),
inference(resolution,[],[f141,f70]) ).
tff(f70,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| number(X1,sK10,one) ),
inference(cnf_transformation,[],[f49]) ).
tff(f49,plain,
( ! [X1: '$ki_world'] :
( ( number(X1,sK10,one)
& entry_box(X1,sK10) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f23,f48]) ).
tff(f48,plain,
( ? [X0] :
( ! [X1: '$ki_world'] :
( ( number(X1,X0,one)
& entry_box(X1,X0) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
& '$ki_exists_in_world_$i'('$ki_local_world',X0) )
=> ( ! [X1: '$ki_world'] :
( ( number(X1,sK10,one)
& entry_box(X1,sK10) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK10) ) ),
introduced(choice_axiom,[]) ).
tff(f23,plain,
? [X0] :
( ! [X1: '$ki_world'] :
( ( number(X1,X0,one)
& entry_box(X1,X0) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
& '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f15]) ).
tff(f15,plain,
? [X0] :
( ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( number(X1,X0,one)
& entry_box(X1,X0) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
? [X6] :
( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( number(X0,X6,one)
& entry_box(X0,X6) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f141,plain,
'$ki_accessible'('$ki_local_world',sK3(sK10,sK8(sK5),sK5)),
inference(resolution,[],[f138,f55]) ).
tff(f55,plain,
'$ki_accessible'('$ki_local_world',sK5),
inference(cnf_transformation,[],[f39]) ).
tff(f39,plain,
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( sP0(X2,X1,sK6(X1,X2,X3,X4),X3,X4)
& '$ki_accessible'(sK5,sK6(X1,X2,X3,X4)) )
| sP1(X2,X1,sK5)
| ~ '$ki_exists_in_world_$i'(sK5,X4) )
| ~ '$ki_exists_in_world_$i'(sK5,X3) )
| ~ '$ki_exists_in_world_$i'(sK5,X2) )
| ~ '$ki_exists_in_world_$i'(sK5,X1) )
& '$ki_accessible'('$ki_local_world',sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f26,f38,f37]) ).
tff(f37,plain,
( ? [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ? [X5: '$ki_world'] :
( sP0(X2,X1,X5,X3,X4)
& '$ki_accessible'(X0,X5) )
| sP1(X2,X1,X0)
| ~ '$ki_exists_in_world_$i'(X0,X4) )
| ~ '$ki_exists_in_world_$i'(X0,X3) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) )
=> ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ? [X5: '$ki_world'] :
( sP0(X2,X1,X5,X3,X4)
& '$ki_accessible'(sK5,X5) )
| sP1(X2,X1,sK5)
| ~ '$ki_exists_in_world_$i'(sK5,X4) )
| ~ '$ki_exists_in_world_$i'(sK5,X3) )
| ~ '$ki_exists_in_world_$i'(sK5,X2) )
| ~ '$ki_exists_in_world_$i'(sK5,X1) )
& '$ki_accessible'('$ki_local_world',sK5) ) ),
introduced(choice_axiom,[]) ).
tff(f38,plain,
! [X1,X2,X3,X4] :
( ? [X5: '$ki_world'] :
( sP0(X2,X1,X5,X3,X4)
& '$ki_accessible'(sK5,X5) )
=> ( sP0(X2,X1,sK6(X1,X2,X3,X4),X3,X4)
& '$ki_accessible'(sK5,sK6(X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f26,plain,
? [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ? [X5: '$ki_world'] :
( sP0(X2,X1,X5,X3,X4)
& '$ki_accessible'(X0,X5) )
| sP1(X2,X1,X0)
| ~ '$ki_exists_in_world_$i'(X0,X4) )
| ~ '$ki_exists_in_world_$i'(X0,X3) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(definition_folding,[],[f17,f25,f24]) ).
tff(f24,plain,
! [X2,X1,X5: '$ki_world',X3,X4] :
( ? [X6] :
( ~ in(X5,X1,X2,X6)
& do(X5,X4,X3,X6)
& '$ki_exists_in_world_$i'(X5,X6) )
| ~ sP0(X2,X1,X5,X3,X4) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f25,plain,
! [X2,X1,X0: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ( ~ number(X7,X2,one)
| ~ entry_box(X7,X2)
| ~ userid(X7,u,X1) )
& '$ki_accessible'(X0,X7) )
| ~ sP1(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f17,plain,
? [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ? [X5: '$ki_world'] :
( ? [X6] :
( ~ in(X5,X1,X2,X6)
& do(X5,X4,X3,X6)
& '$ki_exists_in_world_$i'(X5,X6) )
& '$ki_accessible'(X0,X5) )
| ? [X7: '$ki_world'] :
( ( ~ number(X7,X2,one)
| ~ entry_box(X7,X2)
| ~ userid(X7,u,X1) )
& '$ki_accessible'(X0,X7) )
| ~ '$ki_exists_in_world_$i'(X0,X4) )
| ~ '$ki_exists_in_world_$i'(X0,X3) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f16]) ).
tff(f16,plain,
? [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ? [X5: '$ki_world'] :
( ? [X6] :
( ~ in(X5,X1,X2,X6)
& do(X5,X4,X3,X6)
& '$ki_exists_in_world_$i'(X5,X6) )
& '$ki_accessible'(X0,X5) )
| ? [X7: '$ki_world'] :
( ( ~ number(X7,X2,one)
| ~ entry_box(X7,X2)
| ~ userid(X7,u,X1) )
& '$ki_accessible'(X0,X7) )
| ~ '$ki_exists_in_world_$i'(X0,X4) )
| ~ '$ki_exists_in_world_$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,[],[f10]) ).
tff(f10,plain,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ! [X6] :
( '$ki_exists_in_world_$i'(X5,X6)
=> ( do(X5,X4,X3,X6)
=> in(X5,X1,X2,X6) ) ) )
& ! [X7: '$ki_world'] :
( '$ki_accessible'(X0,X7)
=> ( number(X7,X2,one)
& entry_box(X7,X2)
& userid(X7,u,X1) ) )
& '$ki_exists_in_world_$i'(X0,X4) )
& '$ki_exists_in_world_$i'(X0,X3) )
& '$ki_exists_in_world_$i'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) ) ),
inference(rectify,[],[f9]) ).
tff(f9,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X4] :
( ? [X6] :
( ? [X8] :
( ? [X7] :
( ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ! [X9] :
( '$ki_exists_in_world_$i'(X5,X9)
=> ( do(X5,X7,X8,X9)
=> in(X5,X4,X6,X9) ) ) )
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ( number(X5,X6,one)
& entry_box(X5,X6)
& userid(X5,u,X4) ) )
& '$ki_exists_in_world_$i'(X0,X7) )
& '$ki_exists_in_world_$i'(X0,X8) )
& '$ki_exists_in_world_$i'(X0,X6) )
& '$ki_exists_in_world_$i'(X0,X4) ) ),
inference(negated_conjecture,[],[f8]) ).
tff(f8,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X4] :
( ? [X6] :
( ? [X8] :
( ? [X7] :
( ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ! [X9] :
( '$ki_exists_in_world_$i'(X5,X9)
=> ( do(X5,X7,X8,X9)
=> in(X5,X4,X6,X9) ) ) )
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ( number(X5,X6,one)
& entry_box(X5,X6)
& userid(X5,u,X4) ) )
& '$ki_exists_in_world_$i'(X0,X7) )
& '$ki_exists_in_world_$i'(X0,X8) )
& '$ki_exists_in_world_$i'(X0,X6) )
& '$ki_exists_in_world_$i'(X0,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f138,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(X0,sK5)
| '$ki_accessible'(X0,sK3(sK10,sK8(sK5),sK5)) ),
inference(resolution,[],[f135,f67]) ).
tff(f67,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(X1,X2)
| '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tff(f22,plain,
! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'(X1,X2)
| ~ '$ki_accessible'(X0,X1) ),
inference(flattening,[],[f21]) ).
tff(f21,plain,
! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'(X1,X2)
| ~ '$ki_accessible'(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
tff(f2,axiom,
! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
( ( '$ki_accessible'(X1,X2)
& '$ki_accessible'(X0,X1) )
=> '$ki_accessible'(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
tff(f135,plain,
'$ki_accessible'(sK5,sK3(sK10,sK8(sK5),sK5)),
inference(resolution,[],[f133,f50]) ).
tff(f50,plain,
! [X2: '$ki_world',X0: $i,X1: $i] :
( ~ sP1(X0,X1,X2)
| '$ki_accessible'(X2,sK3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0,X1,X2: '$ki_world'] :
( ( ( ~ number(sK3(X0,X1,X2),X0,one)
| ~ entry_box(sK3(X0,X1,X2),X0)
| ~ userid(sK3(X0,X1,X2),u,X1) )
& '$ki_accessible'(X2,sK3(X0,X1,X2)) )
| ~ sP1(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f30,f31]) ).
tff(f31,plain,
! [X0,X1,X2: '$ki_world'] :
( ? [X3: '$ki_world'] :
( ( ~ number(X3,X0,one)
| ~ entry_box(X3,X0)
| ~ userid(X3,u,X1) )
& '$ki_accessible'(X2,X3) )
=> ( ( ~ number(sK3(X0,X1,X2),X0,one)
| ~ entry_box(sK3(X0,X1,X2),X0)
| ~ userid(sK3(X0,X1,X2),u,X1) )
& '$ki_accessible'(X2,sK3(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f30,plain,
! [X0,X1,X2: '$ki_world'] :
( ? [X3: '$ki_world'] :
( ( ~ number(X3,X0,one)
| ~ entry_box(X3,X0)
| ~ userid(X3,u,X1) )
& '$ki_accessible'(X2,X3) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f29]) ).
tff(f29,plain,
! [X2,X1,X0: '$ki_world'] :
( ? [X7: '$ki_world'] :
( ( ~ number(X7,X2,one)
| ~ entry_box(X7,X2)
| ~ userid(X7,u,X1) )
& '$ki_accessible'(X0,X7) )
| ~ sP1(X2,X1,X0) ),
inference(nnf_transformation,[],[f25]) ).
tff(f133,plain,
sP1(sK10,sK8(sK5),sK5),
inference(duplicate_literal_removal,[],[f132]) ).
tff(f132,plain,
( sP1(sK10,sK8(sK5),sK5)
| sP1(sK10,sK8(sK5),sK5) ),
inference(resolution,[],[f130,f116]) ).
tff(f116,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ~ in(sK6(X0,X1,X2,X3),X0,X1,sK4(X1,X0,sK6(X0,X1,X2,X3),X2,X3))
| sP1(X1,X0,sK5) ),
inference(resolution,[],[f54,f112]) ).
tff(f112,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( sP0(X2,X1,sK6(X1,X2,X3,X4),X3,X4)
| sP1(X2,X1,sK5) ),
inference(subsumption_resolution,[],[f111,f66]) ).
tff(f66,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f14]) ).
tff(f14,plain,
! [X0: '$ki_world',X1] : '$ki_exists_in_world_$i'(X0,X1),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: '$ki_world',X3] : '$ki_exists_in_world_$i'(X0,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f111,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( sP0(X2,X1,sK6(X1,X2,X3,X4),X3,X4)
| sP1(X2,X1,sK5)
| ~ '$ki_exists_in_world_$i'(sK5,X1) ),
inference(subsumption_resolution,[],[f110,f66]) ).
tff(f110,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( sP0(X2,X1,sK6(X1,X2,X3,X4),X3,X4)
| sP1(X2,X1,sK5)
| ~ '$ki_exists_in_world_$i'(sK5,X2)
| ~ '$ki_exists_in_world_$i'(sK5,X1) ),
inference(subsumption_resolution,[],[f109,f66]) ).
tff(f109,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( sP0(X2,X1,sK6(X1,X2,X3,X4),X3,X4)
| sP1(X2,X1,sK5)
| ~ '$ki_exists_in_world_$i'(sK5,X3)
| ~ '$ki_exists_in_world_$i'(sK5,X2)
| ~ '$ki_exists_in_world_$i'(sK5,X1) ),
inference(subsumption_resolution,[],[f57,f66]) ).
tff(f57,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( sP0(X2,X1,sK6(X1,X2,X3,X4),X3,X4)
| sP1(X2,X1,sK5)
| ~ '$ki_exists_in_world_$i'(sK5,X4)
| ~ '$ki_exists_in_world_$i'(sK5,X3)
| ~ '$ki_exists_in_world_$i'(sK5,X2)
| ~ '$ki_exists_in_world_$i'(sK5,X1) ),
inference(cnf_transformation,[],[f39]) ).
tff(f54,plain,
! [X2: '$ki_world',X3: $i,X0: $i,X1: $i,X4: $i] :
( ~ sP0(X0,X1,X2,X3,X4)
| ~ in(X2,X1,X0,sK4(X0,X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f36]) ).
tff(f36,plain,
! [X0,X1,X2: '$ki_world',X3,X4] :
( ( ~ in(X2,X1,X0,sK4(X0,X1,X2,X3,X4))
& do(X2,X4,X3,sK4(X0,X1,X2,X3,X4))
& '$ki_exists_in_world_$i'(X2,sK4(X0,X1,X2,X3,X4)) )
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f34,f35]) ).
tff(f35,plain,
! [X0,X1,X2: '$ki_world',X3,X4] :
( ? [X5] :
( ~ in(X2,X1,X0,X5)
& do(X2,X4,X3,X5)
& '$ki_exists_in_world_$i'(X2,X5) )
=> ( ~ in(X2,X1,X0,sK4(X0,X1,X2,X3,X4))
& do(X2,X4,X3,sK4(X0,X1,X2,X3,X4))
& '$ki_exists_in_world_$i'(X2,sK4(X0,X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f34,plain,
! [X0,X1,X2: '$ki_world',X3,X4] :
( ? [X5] :
( ~ in(X2,X1,X0,X5)
& do(X2,X4,X3,X5)
& '$ki_exists_in_world_$i'(X2,X5) )
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f33]) ).
tff(f33,plain,
! [X2,X1,X5: '$ki_world',X3,X4] :
( ? [X6] :
( ~ in(X5,X1,X2,X6)
& do(X5,X4,X3,X6)
& '$ki_exists_in_world_$i'(X5,X6) )
| ~ sP0(X2,X1,X5,X3,X4) ),
inference(nnf_transformation,[],[f24]) ).
tff(f130,plain,
! [X2: $i,X0: $i,X1: $i] :
( in(sK6(X0,X1,sK7(sK5,X2,sK8(sK5),sK10),X2),sK8(sK5),sK10,sK4(X1,X0,sK6(X0,X1,sK7(sK5,X2,sK8(sK5),sK10),X2),sK7(sK5,X2,sK8(sK5),sK10),X2))
| sP1(X1,X0,sK5) ),
inference(resolution,[],[f127,f79]) ).
tff(f79,plain,
string(sK5,sK8(sK5)),
inference(resolution,[],[f77,f58]) ).
tff(f58,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f77,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK5,X0)
| string(X0,sK8(sK5)) ),
inference(resolution,[],[f62,f73]) ).
tff(f73,plain,
sP2(sK8(sK5),sK5),
inference(resolution,[],[f64,f55]) ).
tff(f64,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| sP2(sK8(X0),X0) ),
inference(cnf_transformation,[],[f45]) ).
tff(f45,plain,
! [X0: '$ki_world'] :
( ( sP2(sK8(X0),X0)
& '$ki_exists_in_world_$i'(X0,sK8(X0)) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f28,f44]) ).
tff(f44,plain,
! [X0: '$ki_world'] :
( ? [X1] :
( sP2(X1,X0)
& '$ki_exists_in_world_$i'(X0,X1) )
=> ( sP2(sK8(X0),X0)
& '$ki_exists_in_world_$i'(X0,sK8(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f28,plain,
! [X0: '$ki_world'] :
( ? [X1] :
( sP2(X1,X0)
& '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(definition_folding,[],[f20,f27]) ).
tff(f27,plain,
! [X1,X0: '$ki_world'] :
( ! [X2: '$ki_world'] :
( ( string(X2,X1)
& userid(X2,u,X1) )
| ~ '$ki_accessible'(X0,X2) )
| ~ sP2(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f20,plain,
! [X0: '$ki_world'] :
( ? [X1] :
( ! [X2: '$ki_world'] :
( ( string(X2,X1)
& userid(X2,u,X1) )
| ~ '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f12]) ).
tff(f12,plain,
! [X0: '$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,[],[f5]) ).
tff(f5,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X4] :
( ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ( string(X5,X4)
& userid(X5,u,X4) ) )
& '$ki_exists_in_world_$i'(X0,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f62,plain,
! [X2: '$ki_world',X0: $i,X1: '$ki_world'] :
( ~ sP2(X0,X1)
| ~ '$ki_accessible'(X1,X2)
| string(X2,X0) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,plain,
! [X0,X1: '$ki_world'] :
( ! [X2: '$ki_world'] :
( ( string(X2,X0)
& userid(X2,u,X0) )
| ~ '$ki_accessible'(X1,X2) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f42]) ).
tff(f42,plain,
! [X1,X0: '$ki_world'] :
( ! [X2: '$ki_world'] :
( ( string(X2,X1)
& userid(X2,u,X1) )
| ~ '$ki_accessible'(X0,X2) )
| ~ sP2(X1,X0) ),
inference(nnf_transformation,[],[f27]) ).
tff(f127,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ~ string(sK5,X3)
| in(sK6(X0,X1,sK7(sK5,X2,X3,sK10),X2),X3,sK10,sK4(X1,X0,sK6(X0,X1,sK7(sK5,X2,X3,sK10),X2),sK7(sK5,X2,X3,sK10),X2))
| sP1(X1,X0,sK5) ),
inference(subsumption_resolution,[],[f126,f93]) ).
tff(f93,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( sP1(X2,X1,sK5)
| '$ki_accessible'(sK5,sK6(X1,X2,X3,X4)) ),
inference(subsumption_resolution,[],[f92,f66]) ).
tff(f92,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( '$ki_accessible'(sK5,sK6(X1,X2,X3,X4))
| sP1(X2,X1,sK5)
| ~ '$ki_exists_in_world_$i'(sK5,X1) ),
inference(subsumption_resolution,[],[f91,f66]) ).
tff(f91,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( '$ki_accessible'(sK5,sK6(X1,X2,X3,X4))
| sP1(X2,X1,sK5)
| ~ '$ki_exists_in_world_$i'(sK5,X2)
| ~ '$ki_exists_in_world_$i'(sK5,X1) ),
inference(subsumption_resolution,[],[f90,f66]) ).
tff(f90,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( '$ki_accessible'(sK5,sK6(X1,X2,X3,X4))
| sP1(X2,X1,sK5)
| ~ '$ki_exists_in_world_$i'(sK5,X3)
| ~ '$ki_exists_in_world_$i'(sK5,X2)
| ~ '$ki_exists_in_world_$i'(sK5,X1) ),
inference(subsumption_resolution,[],[f56,f66]) ).
tff(f56,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( '$ki_accessible'(sK5,sK6(X1,X2,X3,X4))
| sP1(X2,X1,sK5)
| ~ '$ki_exists_in_world_$i'(sK5,X4)
| ~ '$ki_exists_in_world_$i'(sK5,X3)
| ~ '$ki_exists_in_world_$i'(sK5,X2)
| ~ '$ki_exists_in_world_$i'(sK5,X1) ),
inference(cnf_transformation,[],[f39]) ).
tff(f126,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ~ '$ki_accessible'(sK5,sK6(X0,X1,sK7(sK5,X2,X3,sK10),X2))
| in(sK6(X0,X1,sK7(sK5,X2,X3,sK10),X2),X3,sK10,sK4(X1,X0,sK6(X0,X1,sK7(sK5,X2,X3,sK10),X2),sK7(sK5,X2,X3,sK10),X2))
| ~ string(sK5,X3)
| sP1(X1,X0,sK5) ),
inference(subsumption_resolution,[],[f123,f55]) ).
tff(f123,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ~ '$ki_accessible'(sK5,sK6(X0,X1,sK7(sK5,X2,X3,sK10),X2))
| in(sK6(X0,X1,sK7(sK5,X2,X3,sK10),X2),X3,sK10,sK4(X1,X0,sK6(X0,X1,sK7(sK5,X2,X3,sK10),X2),sK7(sK5,X2,X3,sK10),X2))
| ~ string(sK5,X3)
| ~ '$ki_accessible'('$ki_local_world',sK5)
| sP1(X1,X0,sK5) ),
inference(resolution,[],[f122,f71]) ).
tff(f71,plain,
entry_box(sK5,sK10),
inference(resolution,[],[f69,f55]) ).
tff(f69,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| entry_box(X1,sK10) ),
inference(cnf_transformation,[],[f49]) ).
tff(f122,plain,
! [X2: '$ki_world',X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ~ entry_box(X2,X5)
| ~ '$ki_accessible'(X2,sK6(X0,X1,sK7(X2,X3,X4,X5),X3))
| in(sK6(X0,X1,sK7(X2,X3,X4,X5),X3),X4,X5,sK4(X1,X0,sK6(X0,X1,sK7(X2,X3,X4,X5),X3),sK7(X2,X3,X4,X5),X3))
| ~ string(X2,X4)
| ~ '$ki_accessible'('$ki_local_world',X2)
| sP1(X1,X0,sK5) ),
inference(resolution,[],[f121,f115]) ).
tff(f115,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( do(sK6(X0,X1,X2,X3),X3,X2,sK4(X1,X0,sK6(X0,X1,X2,X3),X2,X3))
| sP1(X1,X0,sK5) ),
inference(resolution,[],[f53,f112]) ).
tff(f53,plain,
! [X2: '$ki_world',X3: $i,X0: $i,X1: $i,X4: $i] :
( ~ sP0(X0,X1,X2,X3,X4)
| do(X2,X4,X3,sK4(X0,X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f36]) ).
tff(f121,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( ~ do(X5,X1,sK7(X0,X1,X2,X3),X6)
| in(X5,X2,X3,X6)
| ~ '$ki_accessible'(X0,X5)
| ~ entry_box(X0,X3)
| ~ string(X0,X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f120,f66]) ).
tff(f120,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK7(X0,X1,X2,X3),X6)
| ~ '$ki_accessible'(X0,X5)
| ~ entry_box(X0,X3)
| ~ string(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f119,f66]) ).
tff(f119,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK7(X0,X1,X2,X3),X6)
| ~ '$ki_accessible'(X0,X5)
| ~ entry_box(X0,X3)
| ~ string(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f118,f66]) ).
tff(f118,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK7(X0,X1,X2,X3),X6)
| ~ '$ki_accessible'(X0,X5)
| ~ entry_box(X0,X3)
| ~ string(X0,X2)
| ~ '$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(subsumption_resolution,[],[f60,f66]) ).
tff(f60,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK7(X0,X1,X2,X3),X6)
| ~ '$ki_exists_in_world_$i'(X5,X6)
| ~ '$ki_accessible'(X0,X5)
| ~ entry_box(X0,X3)
| ~ string(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f41]) ).
tff(f41,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ! [X5: '$ki_world'] :
( ! [X6] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK7(X0,X1,X2,X3),X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'(X0,X5) )
& '$ki_exists_in_world_$i'(X0,sK7(X0,X1,X2,X3)) )
| ~ 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(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f19,f40]) ).
tff(f40,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_$i'(X0,X4) )
=> ( ! [X5: '$ki_world'] :
( ! [X6] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK7(X0,X1,X2,X3),X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'(X0,X5) )
& '$ki_exists_in_world_$i'(X0,sK7(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f19,plain,
! [X0: '$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(flattening,[],[f18]) ).
tff(f18,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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f11]) ).
tff(f11,plain,
! [X0: '$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,[],[f7]) ).
tff(f7,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X7] :
( '$ki_exists_in_world_$i'(X0,X7)
=> ! [X4] :
( '$ki_exists_in_world_$i'(X0,X4)
=> ! [X6] :
( '$ki_exists_in_world_$i'(X0,X6)
=> ( ( entry_box(X0,X6)
& string(X0,X4) )
=> ? [X8] :
( ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ! [X9] :
( '$ki_exists_in_world_$i'(X5,X9)
=> ( do(X5,X7,X8,X9)
=> in(X5,X4,X6,X9) ) ) )
& '$ki_exists_in_world_$i'(X0,X8) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f225,plain,
~ number(sK3(sK10,sK8(sK5),sK5),sK10,one),
inference(subsumption_resolution,[],[f224,f136]) ).
tff(f136,plain,
userid(sK3(sK10,sK8(sK5),sK5),u,sK8(sK5)),
inference(resolution,[],[f135,f85]) ).
tff(f85,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK5,X0)
| userid(X0,u,sK8(sK5)) ),
inference(resolution,[],[f61,f73]) ).
tff(f61,plain,
! [X2: '$ki_world',X0: $i,X1: '$ki_world'] :
( ~ sP2(X0,X1)
| ~ '$ki_accessible'(X1,X2)
| userid(X2,u,X0) ),
inference(cnf_transformation,[],[f43]) ).
tff(f224,plain,
( ~ userid(sK3(sK10,sK8(sK5),sK5),u,sK8(sK5))
| ~ number(sK3(sK10,sK8(sK5),sK5),sK10,one) ),
inference(subsumption_resolution,[],[f134,f147]) ).
tff(f147,plain,
entry_box(sK3(sK10,sK8(sK5),sK5),sK10),
inference(resolution,[],[f141,f69]) ).
tff(f134,plain,
( ~ entry_box(sK3(sK10,sK8(sK5),sK5),sK10)
| ~ userid(sK3(sK10,sK8(sK5),sK5),u,sK8(sK5))
| ~ number(sK3(sK10,sK8(sK5),sK5),sK10,one) ),
inference(resolution,[],[f133,f51]) ).
tff(f51,plain,
! [X2: '$ki_world',X0: $i,X1: $i] :
( ~ sP1(X0,X1,X2)
| ~ entry_box(sK3(X0,X1,X2),X0)
| ~ userid(sK3(X0,X1,X2),u,X1)
| ~ number(sK3(X0,X1,X2),X0,one) ),
inference(cnf_transformation,[],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NLP266_4 : TPTP v8.2.0. Released v8.2.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n006.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun May 19 22:34:53 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.37 % (9539)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37 % (9541)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.37 % (9540)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.16/0.37 % (9544)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.16/0.38 TRYING [1,1]
% 0.16/0.38 TRYING [2,1]
% 0.16/0.38 TRYING [1,2]
% 0.16/0.38 TRYING [3,1]
% 0.16/0.38 % (9544)First to succeed.
% 0.16/0.38 Detected minimum model sizes of [1,1,1,1]
% 0.16/0.38 Detected maximum model sizes of [max,max,1,max]
% 0.16/0.38 TRYING [2,2]
% 0.16/0.38 TRYING [1,1,1,1]
% 0.16/0.38 TRYING [2,1,1,1]
% 0.16/0.38 % (9544)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9539"
% 0.16/0.38 TRYING [3,1,1,1]
% 0.16/0.38 % (9544)Refutation found. Thanks to Tanya!
% 0.16/0.38 % SZS status Theorem for theBenchmark
% 0.16/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.38 % (9544)------------------------------
% 0.16/0.38 % (9544)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.38 % (9544)Termination reason: Refutation
% 0.16/0.38
% 0.16/0.38 % (9544)Memory used [KB]: 855
% 0.16/0.38 % (9544)Time elapsed: 0.006 s
% 0.16/0.38 % (9544)Instructions burned: 14 (million)
% 0.16/0.38 % (9539)Success in time 0.013 s
%------------------------------------------------------------------------------