TSTP Solution File: NLP266_23 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NLP266_23 : 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 : n007.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 01:05:44 EDT 2024
% Result : Theorem 0.15s 0.38s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 32
% Syntax : Number of formulae : 88 ( 12 unt; 18 typ; 0 def)
% Number of atoms : 478 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 529 ( 202 ~; 185 |; 98 &)
% ( 0 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 10 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 81 ( 81 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 : 310 ( 259 !; 51 ?; 193 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_3,type,
sK1: ( $i * $i * $i * $i * '$ki_world' ) > '$ki_world' ).
tff(func_def_4,type,
sK2: ( $i * $i * $i * $i * '$ki_world' ) > $i ).
tff(func_def_5,type,
sK3: '$ki_world' ).
tff(func_def_6,type,
sK4: ( $i * $i ) > '$ki_world' ).
tff(func_def_7,type,
sK5: ( '$ki_world' * $i * $i * $i ) > $i ).
tff(func_def_8,type,
sK6: '$ki_world' > $i ).
tff(func_def_9,type,
sK7: '$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 * $i * $i * '$ki_world' ) > $o ).
tff(f82,plain,
$false,
inference(resolution,[],[f81,f70]) ).
tff(f70,plain,
! [X2: $i,X0: '$ki_world',X1: $i] : sP0(sK8,sK6(X0),X1,X2,sK3),
inference(subsumption_resolution,[],[f69,f59]) ).
tff(f59,plain,
! [X1: '$ki_world'] : number(X1,sK8,one),
inference(subsumption_resolution,[],[f57,f53]) ).
tff(f53,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
tff(f57,plain,
! [X1: '$ki_world'] :
( number(X1,sK8,one)
| ~ '$ki_accessible'('$ki_local_world',X1) ),
inference(cnf_transformation,[],[f39]) ).
tff(f39,plain,
( ! [X1: '$ki_world'] :
( ( number(X1,sK8,one)
& entry_box(X1,sK8) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f20,f38]) ).
tff(f38,plain,
( ? [X0] :
( ! [X1: '$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,sK8,one)
& entry_box(X1,sK8) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK8) ) ),
introduced(choice_axiom,[]) ).
tff(f20,plain,
? [X0] :
( ! [X1: '$ki_world'] :
( ( number(X1,X0,one)
& entry_box(X1,X0) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
& '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f14]) ).
tff(f14,plain,
? [X0] :
( ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( number(X1,X0,one)
& entry_box(X1,X0) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
? [X5] :
( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( number(X0,X5,one)
& entry_box(X0,X5) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f69,plain,
! [X2: $i,X0: '$ki_world',X1: $i] :
( ~ number(sK4(sK6(X0),sK8),sK8,one)
| sP0(sK8,sK6(X0),X1,X2,sK3) ),
inference(resolution,[],[f68,f58]) ).
tff(f58,plain,
! [X1: '$ki_world'] : entry_box(X1,sK8),
inference(subsumption_resolution,[],[f56,f53]) ).
tff(f56,plain,
! [X1: '$ki_world'] :
( entry_box(X1,sK8)
| ~ '$ki_accessible'('$ki_local_world',X1) ),
inference(cnf_transformation,[],[f39]) ).
tff(f68,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i] :
( ~ entry_box(sK4(sK6(X0),X1),X1)
| ~ number(sK4(sK6(X0),X1),X1,one)
| sP0(X1,sK6(X0),X2,X3,sK3) ),
inference(resolution,[],[f67,f63]) ).
tff(f63,plain,
! [X2: '$ki_world',X0: '$ki_world'] : userid(X2,u,sK6(X0)),
inference(subsumption_resolution,[],[f62,f53]) ).
tff(f62,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( userid(X2,u,sK6(X0))
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f50,f53]) ).
tff(f50,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( userid(X2,u,sK6(X0))
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f35]) ).
tff(f35,plain,
! [X0: '$ki_world'] :
( ( ! [X2: '$ki_world'] :
( ( string(X2,sK6(X0))
& userid(X2,u,sK6(X0)) )
| ~ '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,sK6(X0)) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f19,f34]) ).
tff(f34,plain,
! [X0: '$ki_world'] :
( ? [X1] :
( ! [X2: '$ki_world'] :
( ( string(X2,X1)
& userid(X2,u,X1) )
| ~ '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
=> ( ! [X2: '$ki_world'] :
( ( string(X2,sK6(X0))
& userid(X2,u,sK6(X0)) )
| ~ '$ki_accessible'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,sK6(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f19,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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f11]) ).
tff(f11,plain,
! [X0: '$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'] :
( '$ki_accessible'(X0,X4)
=> ( string(X4,X3)
& userid(X4,u,X3) ) )
& '$ki_exists_in_world_$i'(X0,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f67,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ userid(sK4(X1,X2),u,X1)
| ~ number(sK4(X1,X2),X2,one)
| ~ entry_box(sK4(X1,X2),X2)
| sP0(X2,X1,X3,X4,sK3) ),
inference(subsumption_resolution,[],[f66,f54]) ).
tff(f54,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f13]) ).
tff(f13,plain,
! [X0: '$ki_world',X1] : '$ki_exists_in_world_$i'(X0,X1),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X0: '$ki_world',X2] : '$ki_exists_in_world_$i'(X0,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f66,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( sP0(X2,X1,X3,X4,sK3)
| ~ number(sK4(X1,X2),X2,one)
| ~ entry_box(sK4(X1,X2),X2)
| ~ userid(sK4(X1,X2),u,X1)
| ~ '$ki_exists_in_world_$i'(sK3,X1) ),
inference(subsumption_resolution,[],[f65,f54]) ).
tff(f65,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( sP0(X2,X1,X3,X4,sK3)
| ~ number(sK4(X1,X2),X2,one)
| ~ entry_box(sK4(X1,X2),X2)
| ~ userid(sK4(X1,X2),u,X1)
| ~ '$ki_exists_in_world_$i'(sK3,X2)
| ~ '$ki_exists_in_world_$i'(sK3,X1) ),
inference(subsumption_resolution,[],[f64,f54]) ).
tff(f64,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( sP0(X2,X1,X3,X4,sK3)
| ~ number(sK4(X1,X2),X2,one)
| ~ entry_box(sK4(X1,X2),X2)
| ~ userid(sK4(X1,X2),u,X1)
| ~ '$ki_exists_in_world_$i'(sK3,X3)
| ~ '$ki_exists_in_world_$i'(sK3,X2)
| ~ '$ki_exists_in_world_$i'(sK3,X1) ),
inference(subsumption_resolution,[],[f46,f54]) ).
tff(f46,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( sP0(X2,X1,X3,X4,sK3)
| ~ number(sK4(X1,X2),X2,one)
| ~ entry_box(sK4(X1,X2),X2)
| ~ userid(sK4(X1,X2),u,X1)
| ~ '$ki_exists_in_world_$i'(sK3,X4)
| ~ '$ki_exists_in_world_$i'(sK3,X3)
| ~ '$ki_exists_in_world_$i'(sK3,X2)
| ~ '$ki_exists_in_world_$i'(sK3,X1) ),
inference(cnf_transformation,[],[f31]) ).
tff(f31,plain,
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( sP0(X2,X1,X3,X4,sK3)
| ( ( ~ number(sK4(X1,X2),X2,one)
| ~ entry_box(sK4(X1,X2),X2)
| ~ userid(sK4(X1,X2),u,X1) )
& '$ki_accessible'(sK3,sK4(X1,X2)) )
| ~ '$ki_exists_in_world_$i'(sK3,X4) )
| ~ '$ki_exists_in_world_$i'(sK3,X3) )
| ~ '$ki_exists_in_world_$i'(sK3,X2) )
| ~ '$ki_exists_in_world_$i'(sK3,X1) )
& '$ki_accessible'('$ki_local_world',sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f28,f30,f29]) ).
tff(f29,plain,
( ? [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( sP0(X2,X1,X3,X4,X0)
| ? [X5: '$ki_world'] :
( ( ~ number(X5,X2,one)
| ~ entry_box(X5,X2)
| ~ userid(X5,u,X1) )
& '$ki_accessible'(X0,X5) )
| ~ '$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'('$ki_local_world',X0) )
=> ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( sP0(X2,X1,X3,X4,sK3)
| ? [X5: '$ki_world'] :
( ( ~ number(X5,X2,one)
| ~ entry_box(X5,X2)
| ~ userid(X5,u,X1) )
& '$ki_accessible'(sK3,X5) )
| ~ '$ki_exists_in_world_$i'(sK3,X4) )
| ~ '$ki_exists_in_world_$i'(sK3,X3) )
| ~ '$ki_exists_in_world_$i'(sK3,X2) )
| ~ '$ki_exists_in_world_$i'(sK3,X1) )
& '$ki_accessible'('$ki_local_world',sK3) ) ),
introduced(choice_axiom,[]) ).
tff(f30,plain,
! [X1,X2] :
( ? [X5: '$ki_world'] :
( ( ~ number(X5,X2,one)
| ~ entry_box(X5,X2)
| ~ userid(X5,u,X1) )
& '$ki_accessible'(sK3,X5) )
=> ( ( ~ number(sK4(X1,X2),X2,one)
| ~ entry_box(sK4(X1,X2),X2)
| ~ userid(sK4(X1,X2),u,X1) )
& '$ki_accessible'(sK3,sK4(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f28,plain,
? [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( sP0(X2,X1,X3,X4,X0)
| ? [X5: '$ki_world'] :
( ( ~ number(X5,X2,one)
| ~ entry_box(X5,X2)
| ~ userid(X5,u,X1) )
& '$ki_accessible'(X0,X5) )
| ~ '$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'('$ki_local_world',X0) ),
inference(rectify,[],[f22]) ).
tff(f22,plain,
? [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( sP0(X2,X1,X3,X4,X0)
| ? [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(definition_folding,[],[f16,f21]) ).
tff(f21,plain,
! [X2,X1,X3,X4,X0: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ? [X6] :
( ~ in(X5,X1,X2,X6)
& do(X5,X4,X3,X6)
& '$ki_exists_in_world_$i'(X5,X6) )
& '$ki_accessible'(X0,X5) )
| ~ sP0(X2,X1,X3,X4,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f16,plain,
? [X0: '$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(flattening,[],[f15]) ).
tff(f15,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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f9,plain,
~ ! [X0: '$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,[],[f8]) ).
tff(f8,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X3] :
( ? [X5] :
( ? [X7] :
( ? [X6] :
( ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ! [X8] :
( '$ki_exists_in_world_$i'(X4,X8)
=> ( do(X4,X6,X7,X8)
=> in(X4,X3,X5,X8) ) ) )
& ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ( number(X4,X5,one)
& entry_box(X4,X5)
& userid(X4,u,X3) ) )
& '$ki_exists_in_world_$i'(X0,X6) )
& '$ki_exists_in_world_$i'(X0,X7) )
& '$ki_exists_in_world_$i'(X0,X5) )
& '$ki_exists_in_world_$i'(X0,X3) ) ),
inference(negated_conjecture,[],[f7]) ).
tff(f7,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X3] :
( ? [X5] :
( ? [X7] :
( ? [X6] :
( ! [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) ) ) )
& ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ( number(X4,X5,one)
& entry_box(X4,X5)
& userid(X4,u,X3) ) )
& '$ki_exists_in_world_$i'(X0,X6) )
& '$ki_exists_in_world_$i'(X0,X7) )
& '$ki_exists_in_world_$i'(X0,X5) )
& '$ki_exists_in_world_$i'(X0,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f81,plain,
! [X2: $i,X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] : ~ sP0(sK8,sK6(X0),sK5(X1,X2,sK6(X0),sK8),X2,X3),
inference(duplicate_literal_removal,[],[f80]) ).
tff(f80,plain,
! [X2: $i,X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( ~ sP0(sK8,sK6(X0),sK5(X1,X2,sK6(X0),sK8),X2,X3)
| ~ sP0(sK8,sK6(X0),sK5(X1,X2,sK6(X0),sK8),X2,X3) ),
inference(resolution,[],[f79,f43]) ).
tff(f43,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: '$ki_world'] :
( ~ in(sK1(X0,X1,X2,X3,X4),X1,X0,sK2(X0,X1,X2,X3,X4))
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f27]) ).
tff(f27,plain,
! [X0,X1,X2,X3,X4: '$ki_world'] :
( ( ~ in(sK1(X0,X1,X2,X3,X4),X1,X0,sK2(X0,X1,X2,X3,X4))
& do(sK1(X0,X1,X2,X3,X4),X3,X2,sK2(X0,X1,X2,X3,X4))
& '$ki_exists_in_world_$i'(sK1(X0,X1,X2,X3,X4),sK2(X0,X1,X2,X3,X4))
& '$ki_accessible'(X4,sK1(X0,X1,X2,X3,X4)) )
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f24,f26,f25]) ).
tff(f25,plain,
! [X0,X1,X2,X3,X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ? [X6] :
( ~ in(X5,X1,X0,X6)
& do(X5,X3,X2,X6)
& '$ki_exists_in_world_$i'(X5,X6) )
& '$ki_accessible'(X4,X5) )
=> ( ? [X6] :
( ~ in(sK1(X0,X1,X2,X3,X4),X1,X0,X6)
& do(sK1(X0,X1,X2,X3,X4),X3,X2,X6)
& '$ki_exists_in_world_$i'(sK1(X0,X1,X2,X3,X4),X6) )
& '$ki_accessible'(X4,sK1(X0,X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f26,plain,
! [X0,X1,X2,X3,X4: '$ki_world'] :
( ? [X6] :
( ~ in(sK1(X0,X1,X2,X3,X4),X1,X0,X6)
& do(sK1(X0,X1,X2,X3,X4),X3,X2,X6)
& '$ki_exists_in_world_$i'(sK1(X0,X1,X2,X3,X4),X6) )
=> ( ~ in(sK1(X0,X1,X2,X3,X4),X1,X0,sK2(X0,X1,X2,X3,X4))
& do(sK1(X0,X1,X2,X3,X4),X3,X2,sK2(X0,X1,X2,X3,X4))
& '$ki_exists_in_world_$i'(sK1(X0,X1,X2,X3,X4),sK2(X0,X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f24,plain,
! [X0,X1,X2,X3,X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ? [X6] :
( ~ in(X5,X1,X0,X6)
& do(X5,X3,X2,X6)
& '$ki_exists_in_world_$i'(X5,X6) )
& '$ki_accessible'(X4,X5) )
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f23]) ).
tff(f23,plain,
! [X2,X1,X3,X4,X0: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ? [X6] :
( ~ in(X5,X1,X2,X6)
& do(X5,X4,X3,X6)
& '$ki_exists_in_world_$i'(X5,X6) )
& '$ki_accessible'(X0,X5) )
| ~ sP0(X2,X1,X3,X4,X0) ),
inference(nnf_transformation,[],[f21]) ).
tff(f79,plain,
! [X2: '$ki_world',X3: $i,X0: $i,X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( in(sK1(X0,X1,sK5(X2,X3,sK6(X4),sK8),X3,X5),sK6(X4),sK8,sK2(X0,X1,sK5(X2,X3,sK6(X4),sK8),X3,X5))
| ~ sP0(X0,X1,sK5(X2,X3,sK6(X4),sK8),X3,X5) ),
inference(resolution,[],[f78,f42]) ).
tff(f42,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: '$ki_world'] :
( do(sK1(X0,X1,X2,X3,X4),X3,X2,sK2(X0,X1,X2,X3,X4))
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f27]) ).
tff(f78,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: '$ki_world',X4: '$ki_world'] :
( ~ do(X0,X3,sK5(X4,X3,sK6(X1),sK8),X2)
| in(X0,sK6(X1),sK8,X2) ),
inference(resolution,[],[f77,f61]) ).
tff(f61,plain,
! [X2: '$ki_world',X0: '$ki_world'] : string(X2,sK6(X0)),
inference(subsumption_resolution,[],[f60,f53]) ).
tff(f60,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( string(X2,sK6(X0))
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f51,f53]) ).
tff(f51,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( string(X2,sK6(X0))
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f35]) ).
tff(f77,plain,
! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: $i] :
( ~ string(X2,X3)
| in(X0,X3,sK8,X4)
| ~ do(X0,X1,sK5(X2,X1,X3,sK8),X4) ),
inference(resolution,[],[f76,f58]) ).
tff(f76,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( ~ entry_box(X0,X3)
| ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
| in(X5,X2,X3,X6)
| ~ string(X0,X2) ),
inference(subsumption_resolution,[],[f75,f53]) ).
tff(f75,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
| ~ entry_box(X0,X3)
| ~ string(X0,X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f74,f54]) ).
tff(f74,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
| ~ entry_box(X0,X3)
| ~ string(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f73,f54]) ).
tff(f73,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
| ~ 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,[],[f72,f54]) ).
tff(f72,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
| ~ 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,[],[f71,f53]) ).
tff(f71,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK5(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,[],[f48,f54]) ).
tff(f48,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK5(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'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f33]) ).
tff(f33,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ! [X5: '$ki_world'] :
( ! [X6] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'(X0,X5) )
& '$ki_exists_in_world_$i'(X0,sK5(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,[sK5])],[f18,f32]) ).
tff(f32,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,sK5(X0,X1,X2,X3),X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'(X0,X5) )
& '$ki_exists_in_world_$i'(X0,sK5(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f18,plain,
! [X0: '$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(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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f10]) ).
tff(f10,plain,
! [X0: '$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_$i'(X0,X5)
=> ( ( entry_box(X0,X5)
& string(X0,X3) )
=> ? [X7] :
( ! [X4: '$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/sandbox2/benchmark/theBenchmark.p',ax3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NLP266_23 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 22:12:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (21990)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (21991)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.38 % (21992)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (21993)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)
% 0.15/0.38 % (21994)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.38 % (21996)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.38 % (21997)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)
% 0.15/0.38 % (21995)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.38 % (21996)First to succeed.
% 0.15/0.38 % (21995)Also succeeded, but the first one will report.
% 0.15/0.38 TRYING [1,1]
% 0.15/0.38 TRYING [2,1]
% 0.15/0.38 TRYING [1,1]
% 0.15/0.38 Detected minimum model sizes of [1,1,1,1]
% 0.15/0.38 Detected maximum model sizes of [max,max,1,max]
% 0.15/0.38 TRYING [1,1,1,1]
% 0.15/0.38 TRYING [2,1]
% 0.15/0.38 TRYING [1,2]
% 0.15/0.38 % (21996)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21990"
% 0.15/0.38 TRYING [2,1,1,1]
% 0.15/0.38 TRYING [1,2]
% 0.15/0.38 TRYING [3,1,1,1]
% 0.15/0.38 % (21996)Refutation found. Thanks to Tanya!
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38 % (21996)------------------------------
% 0.15/0.38 % (21996)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38 % (21996)Termination reason: Refutation
% 0.15/0.38
% 0.15/0.38 % (21996)Memory used [KB]: 816
% 0.15/0.38 % (21996)Time elapsed: 0.006 s
% 0.15/0.38 % (21996)Instructions burned: 8 (million)
% 0.15/0.38 % (21990)Success in time 0.022 s
%------------------------------------------------------------------------------