TSTP Solution File: PLA054_4 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : PLA054_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 : n026.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 02:21:49 EDT 2024
% Result : Theorem 0.14s 0.37s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 28
% Syntax : Number of formulae : 78 ( 13 unt; 15 typ; 0 def)
% Number of atoms : 373 ( 0 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 433 ( 169 ~; 163 |; 61 &)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 46 ( 46 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 25 ( 12 >; 13 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 4 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 195 ( 172 !; 23 ?; 135 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_4,type,
sK3: '$ki_world' > '$ki_world' ).
tff(func_def_5,type,
sK4: '$ki_world' ).
tff(func_def_6,type,
sK5: ( $i * $i * '$ki_world' ) > $i ).
tff(func_def_7,type,
sK6: '$ki_world' > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
h: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
closed: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
combo: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_5,type,
open: ( '$ki_world' * $i ) > $o ).
tff(pred_def_6,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(pred_def_7,type,
sP0: ( $i * $i * '$ki_world' ) > $o ).
tff(pred_def_8,type,
sP1: '$ki_world' > $o ).
tff(pred_def_9,type,
sP2: ( $i * $i * '$ki_world' ) > $o ).
tff(f130,plain,
$false,
inference(subsumption_resolution,[],[f129,f54]) ).
tff(f54,plain,
'$ki_accessible'('$ki_local_world',sK4),
inference(cnf_transformation,[],[f41]) ).
tff(f41,plain,
( ! [X1] :
( ! [X2] :
( ( sP1(sK4)
& sP0(X2,X1,sK4) )
| ~ '$ki_exists_in_world_$i'(sK4,X2) )
| ~ '$ki_exists_in_world_$i'(sK4,X1) )
& '$ki_accessible'('$ki_local_world',sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f31,f40]) ).
tff(f40,plain,
( ? [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ( sP1(X0)
& sP0(X2,X1,X0) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) )
=> ( ! [X1] :
( ! [X2] :
( ( sP1(sK4)
& sP0(X2,X1,sK4) )
| ~ '$ki_exists_in_world_$i'(sK4,X2) )
| ~ '$ki_exists_in_world_$i'(sK4,X1) )
& '$ki_accessible'('$ki_local_world',sK4) ) ),
introduced(choice_axiom,[]) ).
tff(f31,plain,
? [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ( sP1(X0)
& sP0(X2,X1,X0) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(definition_folding,[],[f18,f30,f29]) ).
tff(f29,plain,
! [X2,X1,X0: '$ki_world'] :
( ! [X3: '$ki_world'] :
( ( h(X3,X2)
& combo(X3,d,X1) )
| ~ '$ki_accessible'(X0,X3) )
| ~ sP0(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f30,plain,
! [X0: '$ki_world'] :
( ? [X4: '$ki_world'] :
( ~ open(X4,d)
& '$ki_accessible'(X0,X4) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f18,plain,
? [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ( ? [X4: '$ki_world'] :
( ~ open(X4,d)
& '$ki_accessible'(X0,X4) )
& ! [X3: '$ki_world'] :
( ( h(X3,X2)
& combo(X3,d,X1) )
| ~ '$ki_accessible'(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,[],[f12]) ).
tff(f12,plain,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1] :
( ? [X2] :
( ( ! [X3: '$ki_world'] :
( '$ki_accessible'(X0,X3)
=> ( h(X3,X2)
& combo(X3,d,X1) ) )
=> ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> open(X4,d) ) )
& '$ki_exists_in_world_$i'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) ) ),
inference(rectify,[],[f11]) ).
tff(f11,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1] :
( ? [X5] :
( ( ! [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
=> ( h(X6,X5)
& combo(X6,d,X1) ) )
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
=> open(X6,d) ) )
& '$ki_exists_in_world_$i'(X0,X5) )
& '$ki_exists_in_world_$i'(X0,X1) ) ),
inference(negated_conjecture,[],[f10]) ).
tff(f10,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1] :
( ? [X5] :
( ( ! [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
=> ( h(X6,X5)
& combo(X6,d,X1) ) )
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
=> open(X6,d) ) )
& '$ki_exists_in_world_$i'(X0,X5) )
& '$ki_exists_in_world_$i'(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f129,plain,
~ '$ki_accessible'('$ki_local_world',sK4),
inference(subsumption_resolution,[],[f128,f75]) ).
tff(f75,plain,
closed(sK4,d),
inference(resolution,[],[f58,f54]) ).
tff(f58,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| closed(X0,d) ),
inference(cnf_transformation,[],[f19]) ).
tff(f19,plain,
! [X0: '$ki_world'] :
( closed(X0,d)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f6]) ).
tff(f6,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> closed(X0,d) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f128,plain,
( ~ closed(sK4,d)
| ~ '$ki_accessible'('$ki_local_world',sK4) ),
inference(resolution,[],[f127,f95]) ).
tff(f95,plain,
! [X0: '$ki_world',X1: $i] :
( ~ open(X0,X1)
| ~ closed(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f60,f66]) ).
tff(f66,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f16]) ).
tff(f16,plain,
! [X0: '$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_$i_const') ).
tff(f60,plain,
! [X0: '$ki_world',X1: $i] :
( ~ closed(X0,X1)
| ~ open(X0,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f23]) ).
tff(f23,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ~ closed(X0,X1)
| ~ open(X0,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f22]) ).
tff(f22,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ~ closed(X0,X1)
| ~ open(X0,X1)
| ~ '$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)
=> ~ ( closed(X0,X1)
& open(X0,X1) ) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X4] :
( '$ki_exists_in_world_$i'(X0,X4)
=> ~ ( closed(X0,X4)
& open(X0,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f127,plain,
open(sK4,d),
inference(resolution,[],[f118,f57]) ).
tff(f57,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f118,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK4,X0)
| open(X0,d) ),
inference(subsumption_resolution,[],[f117,f57]) ).
tff(f117,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK4,X0)
| ~ '$ki_accessible'(sK4,sK4)
| open(X0,d) ),
inference(subsumption_resolution,[],[f112,f75]) ).
tff(f112,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK4,X0)
| ~ closed(sK4,d)
| ~ '$ki_accessible'(sK4,sK4)
| open(X0,d) ),
inference(resolution,[],[f111,f77]) ).
tff(f77,plain,
combo(sK4,d,sK7),
inference(resolution,[],[f69,f54]) ).
tff(f69,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| combo(X1,d,sK7) ),
inference(cnf_transformation,[],[f49]) ).
tff(f49,plain,
( ! [X1: '$ki_world'] :
( combo(X1,d,sK7)
| ~ '$ki_accessible'('$ki_local_world',X1) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f28,f48]) ).
tff(f48,plain,
( ? [X0] :
( ! [X1: '$ki_world'] :
( combo(X1,d,X0)
| ~ '$ki_accessible'('$ki_local_world',X1) )
& '$ki_exists_in_world_$i'('$ki_local_world',X0) )
=> ( ! [X1: '$ki_world'] :
( combo(X1,d,sK7)
| ~ '$ki_accessible'('$ki_local_world',X1) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK7) ) ),
introduced(choice_axiom,[]) ).
tff(f28,plain,
? [X0] :
( ! [X1: '$ki_world'] :
( combo(X1,d,X0)
| ~ '$ki_accessible'('$ki_local_world',X1) )
& '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f17]) ).
tff(f17,plain,
? [X0] :
( ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> combo(X1,d,X0) )
& '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
? [X1] :
( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> combo(X0,d,X1) )
& '$ki_exists_in_world_$i'('$ki_local_world',X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(f111,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: '$ki_world'] :
( ~ combo(X0,X2,X3)
| ~ '$ki_accessible'(X0,X1)
| ~ closed(X0,X2)
| ~ '$ki_accessible'(sK4,X0)
| open(X1,X2) ),
inference(subsumption_resolution,[],[f108,f88]) ).
tff(f88,plain,
! [X0: '$ki_world',X1: $i] :
( ~ '$ki_accessible'(sK4,X0)
| h(X0,X1) ),
inference(resolution,[],[f53,f73]) ).
tff(f73,plain,
! [X2: $i,X1: $i] : sP0(X2,X1,sK4),
inference(subsumption_resolution,[],[f72,f66]) ).
tff(f72,plain,
! [X2: $i,X1: $i] :
( sP0(X2,X1,sK4)
| ~ '$ki_exists_in_world_$i'(sK4,X1) ),
inference(subsumption_resolution,[],[f55,f66]) ).
tff(f55,plain,
! [X2: $i,X1: $i] :
( sP0(X2,X1,sK4)
| ~ '$ki_exists_in_world_$i'(sK4,X2)
| ~ '$ki_exists_in_world_$i'(sK4,X1) ),
inference(cnf_transformation,[],[f41]) ).
tff(f53,plain,
! [X2: '$ki_world',X3: '$ki_world',X0: $i,X1: $i] :
( ~ sP0(X0,X1,X2)
| ~ '$ki_accessible'(X2,X3)
| h(X3,X0) ),
inference(cnf_transformation,[],[f39]) ).
tff(f39,plain,
! [X0,X1,X2: '$ki_world'] :
( ! [X3: '$ki_world'] :
( ( h(X3,X0)
& combo(X3,d,X1) )
| ~ '$ki_accessible'(X2,X3) )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f38]) ).
tff(f38,plain,
! [X2,X1,X0: '$ki_world'] :
( ! [X3: '$ki_world'] :
( ( h(X3,X2)
& combo(X3,d,X1) )
| ~ '$ki_accessible'(X0,X3) )
| ~ sP0(X2,X1,X0) ),
inference(nnf_transformation,[],[f29]) ).
tff(f108,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| ~ h(X0,sK5(X2,X3,sK4))
| ~ combo(X0,X2,X3)
| ~ closed(X0,X2)
| ~ '$ki_accessible'(sK4,X0)
| open(X1,X2) ),
inference(resolution,[],[f62,f98]) ).
tff(f98,plain,
! [X0: $i,X1: $i] : sP2(X0,X1,sK4),
inference(resolution,[],[f97,f54]) ).
tff(f97,plain,
! [X2: $i,X0: '$ki_world',X1: $i] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| sP2(X1,X2,X0) ),
inference(subsumption_resolution,[],[f96,f66]) ).
tff(f96,plain,
! [X2: $i,X0: '$ki_world',X1: $i] :
( sP2(X1,X2,X0)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f64,f66]) ).
tff(f64,plain,
! [X2: $i,X0: '$ki_world',X1: $i] :
( sP2(X1,X2,X0)
| ~ '$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] :
( sP2(X1,X2,X0)
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(definition_folding,[],[f25,f32]) ).
tff(f32,plain,
! [X1,X2,X0: '$ki_world'] :
( ? [X3] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( closed(X5,X1)
| ~ '$ki_accessible'(X4,X5) )
| ~ h(X4,o)
| combo(X4,X1,X2)
| ~ closed(X4,X1)
| ~ '$ki_accessible'(X0,X4) )
& ! [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( open(X7,X1)
| ~ '$ki_accessible'(X6,X7) )
| ~ h(X6,X3)
| ~ combo(X6,X1,X2)
| ~ closed(X6,X1)
| ~ '$ki_accessible'(X0,X6) )
& '$ki_exists_in_world_$i'(X0,X3) )
| ~ sP2(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f25,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ? [X3] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( closed(X5,X1)
| ~ '$ki_accessible'(X4,X5) )
| ~ h(X4,o)
| combo(X4,X1,X2)
| ~ closed(X4,X1)
| ~ '$ki_accessible'(X0,X4) )
& ! [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( open(X7,X1)
| ~ '$ki_accessible'(X6,X7) )
| ~ h(X6,X3)
| ~ combo(X6,X1,X2)
| ~ closed(X6,X1)
| ~ '$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(flattening,[],[f24]) ).
tff(f24,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2] :
( ? [X3] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( closed(X5,X1)
| ~ '$ki_accessible'(X4,X5) )
| ~ h(X4,o)
| combo(X4,X1,X2)
| ~ closed(X4,X1)
| ~ '$ki_accessible'(X0,X4) )
& ! [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( open(X7,X1)
| ~ '$ki_accessible'(X6,X7) )
| ~ h(X6,X3)
| ~ combo(X6,X1,X2)
| ~ closed(X6,X1)
| ~ '$ki_accessible'(X0,X6) )
& '$ki_exists_in_world_$i'(X0,X3) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f14]) ).
tff(f14,plain,
! [X0: '$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: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ( ( h(X4,o)
& ~ combo(X4,X1,X2)
& closed(X4,X1) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> closed(X5,X1) ) ) )
& ! [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
=> ( ( h(X6,X3)
& combo(X6,X1,X2)
& closed(X6,X1) )
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> open(X7,X1) ) ) )
& '$ki_exists_in_world_$i'(X0,X3) ) ) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X4] :
( '$ki_exists_in_world_$i'(X0,X4)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X5] :
( ! [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
=> ( ( h(X6,o)
& ~ combo(X6,X4,X1)
& closed(X6,X4) )
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> closed(X7,X4) ) ) )
& ! [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
=> ( ( h(X6,X5)
& combo(X6,X4,X1)
& closed(X6,X4) )
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> open(X7,X4) ) ) )
& '$ki_exists_in_world_$i'(X0,X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f62,plain,
! [X2: '$ki_world',X0: $i,X1: $i,X6: '$ki_world',X7: '$ki_world'] :
( ~ sP2(X0,X1,X2)
| ~ '$ki_accessible'(X6,X7)
| ~ h(X6,sK5(X0,X1,X2))
| ~ combo(X6,X0,X1)
| ~ closed(X6,X0)
| ~ '$ki_accessible'(X2,X6)
| open(X7,X0) ),
inference(cnf_transformation,[],[f45]) ).
tff(f45,plain,
! [X0,X1,X2: '$ki_world'] :
( ( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( closed(X5,X0)
| ~ '$ki_accessible'(X4,X5) )
| ~ h(X4,o)
| combo(X4,X0,X1)
| ~ closed(X4,X0)
| ~ '$ki_accessible'(X2,X4) )
& ! [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( open(X7,X0)
| ~ '$ki_accessible'(X6,X7) )
| ~ h(X6,sK5(X0,X1,X2))
| ~ combo(X6,X0,X1)
| ~ closed(X6,X0)
| ~ '$ki_accessible'(X2,X6) )
& '$ki_exists_in_world_$i'(X2,sK5(X0,X1,X2)) )
| ~ sP2(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f43,f44]) ).
tff(f44,plain,
! [X0,X1,X2: '$ki_world'] :
( ? [X3] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( closed(X5,X0)
| ~ '$ki_accessible'(X4,X5) )
| ~ h(X4,o)
| combo(X4,X0,X1)
| ~ closed(X4,X0)
| ~ '$ki_accessible'(X2,X4) )
& ! [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( open(X7,X0)
| ~ '$ki_accessible'(X6,X7) )
| ~ h(X6,X3)
| ~ combo(X6,X0,X1)
| ~ closed(X6,X0)
| ~ '$ki_accessible'(X2,X6) )
& '$ki_exists_in_world_$i'(X2,X3) )
=> ( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( closed(X5,X0)
| ~ '$ki_accessible'(X4,X5) )
| ~ h(X4,o)
| combo(X4,X0,X1)
| ~ closed(X4,X0)
| ~ '$ki_accessible'(X2,X4) )
& ! [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( open(X7,X0)
| ~ '$ki_accessible'(X6,X7) )
| ~ h(X6,sK5(X0,X1,X2))
| ~ combo(X6,X0,X1)
| ~ closed(X6,X0)
| ~ '$ki_accessible'(X2,X6) )
& '$ki_exists_in_world_$i'(X2,sK5(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f43,plain,
! [X0,X1,X2: '$ki_world'] :
( ? [X3] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( closed(X5,X0)
| ~ '$ki_accessible'(X4,X5) )
| ~ h(X4,o)
| combo(X4,X0,X1)
| ~ closed(X4,X0)
| ~ '$ki_accessible'(X2,X4) )
& ! [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( open(X7,X0)
| ~ '$ki_accessible'(X6,X7) )
| ~ h(X6,X3)
| ~ combo(X6,X0,X1)
| ~ closed(X6,X0)
| ~ '$ki_accessible'(X2,X6) )
& '$ki_exists_in_world_$i'(X2,X3) )
| ~ sP2(X0,X1,X2) ),
inference(rectify,[],[f42]) ).
tff(f42,plain,
! [X1,X2,X0: '$ki_world'] :
( ? [X3] :
( ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( closed(X5,X1)
| ~ '$ki_accessible'(X4,X5) )
| ~ h(X4,o)
| combo(X4,X1,X2)
| ~ closed(X4,X1)
| ~ '$ki_accessible'(X0,X4) )
& ! [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( open(X7,X1)
| ~ '$ki_accessible'(X6,X7) )
| ~ h(X6,X3)
| ~ combo(X6,X1,X2)
| ~ closed(X6,X1)
| ~ '$ki_accessible'(X0,X6) )
& '$ki_exists_in_world_$i'(X0,X3) )
| ~ sP2(X1,X2,X0) ),
inference(nnf_transformation,[],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PLA054_4 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat May 18 13:44:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (2189)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (2196)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)
% 0.14/0.37 % (2191)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (2190)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37 % (2193)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.37 % (2195)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37 % (2192)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)
% 0.14/0.37 % (2194)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.37 TRYING [1,1]
% 0.14/0.37 TRYING [2,1]
% 0.14/0.37 TRYING [1,2]
% 0.14/0.37 TRYING [2,2]
% 0.14/0.37 TRYING [1,1]
% 0.14/0.37 TRYING [2,1]
% 0.14/0.37 % (2194)First to succeed.
% 0.14/0.37 TRYING [1,3]
% 0.14/0.37 Detected minimum model sizes of [1,1]
% 0.14/0.37 Detected maximum model sizes of [3,max]
% 0.14/0.37 TRYING [1,1]
% 0.14/0.37 Detected minimum model sizes of [1,1]
% 0.14/0.37 Detected maximum model sizes of [3,max]
% 0.14/0.37 TRYING [1,1]
% 0.14/0.37 TRYING [1,2]
% 0.14/0.37 TRYING [2,1]
% 0.14/0.37 TRYING [2,1]
% 0.14/0.37 TRYING [2,2]
% 0.14/0.37 TRYING [2,3]
% 0.14/0.37 % (2195)Also succeeded, but the first one will report.
% 0.14/0.37 TRYING [1,2]
% 0.14/0.37 TRYING [1,2]
% 0.14/0.37 TRYING [2,2]
% 0.14/0.37 % (2194)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2189"
% 0.14/0.37 TRYING [2,2]
% 0.14/0.37 TRYING [1,3]
% 0.14/0.37 % (2194)Refutation found. Thanks to Tanya!
% 0.14/0.37 % SZS status Theorem for theBenchmark
% 0.14/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.37 % (2194)------------------------------
% 0.14/0.37 % (2194)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37 % (2194)Termination reason: Refutation
% 0.14/0.37
% 0.14/0.37 % (2194)Memory used [KB]: 827
% 0.14/0.37 % (2194)Time elapsed: 0.006 s
% 0.14/0.37 % (2194)Instructions burned: 7 (million)
% 0.14/0.37 % (2189)Success in time 0.021 s
%------------------------------------------------------------------------------