TSTP Solution File: PLA053_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : PLA053_5 : 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 : n025.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 0.22s 0.38s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 50 ( 11 unt; 12 typ; 0 def)
% Number of atoms : 159 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 170 ( 60 ~; 51 |; 39 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 17 ( 9 >; 8 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 95 ( 77 !; 18 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_1,type,
sK1: '$ki_world' ).
tff(func_def_3,type,
sK3: ( '$ki_world' * $i ) > $i ).
tff(func_def_4,type,
sK4: '$ki_world' > $i ).
tff(func_def_5,type,
sK5: '$ki_world' > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
h: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
bomb: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
defused: ( '$ki_world' * $i ) > $o ).
tff(pred_def_5,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(pred_def_6,type,
sP0: ( $i * '$ki_world' * $i ) > $o ).
tff(f74,plain,
$false,
inference(subsumption_resolution,[],[f73,f55]) ).
tff(f55,plain,
~ defused(sK1,sK2),
inference(resolution,[],[f39,f52]) ).
tff(f52,plain,
! [X2: $i] : sP0(sK2,sK1,X2),
inference(subsumption_resolution,[],[f42,f49]) ).
tff(f49,plain,
! [X0: '$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_$i'(X0,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f42,plain,
! [X2: $i] :
( sP0(sK2,sK1,X2)
| ~ '$ki_exists_in_world_$i'(sK1,X2) ),
inference(cnf_transformation,[],[f28]) ).
tff(f28,plain,
( ! [X2] :
( sP0(sK2,sK1,X2)
| ~ '$ki_exists_in_world_$i'(sK1,X2) )
& '$ki_exists_in_world_$i'(sK1,sK2)
& '$ki_accessible'('$ki_local_world',sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f23,f27,f26]) ).
tff(f26,plain,
( ? [X0: '$ki_world'] :
( ? [X1] :
( ! [X2] :
( sP0(X1,X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) )
=> ( ? [X1] :
( ! [X2] :
( sP0(X1,sK1,X2)
| ~ '$ki_exists_in_world_$i'(sK1,X2) )
& '$ki_exists_in_world_$i'(sK1,X1) )
& '$ki_accessible'('$ki_local_world',sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f27,plain,
( ? [X1] :
( ! [X2] :
( sP0(X1,sK1,X2)
| ~ '$ki_exists_in_world_$i'(sK1,X2) )
& '$ki_exists_in_world_$i'(sK1,X1) )
=> ( ! [X2] :
( sP0(sK2,sK1,X2)
| ~ '$ki_exists_in_world_$i'(sK1,X2) )
& '$ki_exists_in_world_$i'(sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f23,plain,
? [X0: '$ki_world'] :
( ? [X1] :
( ! [X2] :
( sP0(X1,X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(definition_folding,[],[f16,f22]) ).
tff(f22,plain,
! [X1,X0: '$ki_world',X2] :
( ( ~ defused(X0,X1)
& h(X0,X2)
& bomb(X0,X1) )
| ~ sP0(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f16,plain,
? [X0: '$ki_world'] :
( ? [X1] :
( ! [X2] :
( ( ~ defused(X0,X1)
& h(X0,X2)
& bomb(X0,X1) )
| ~ '$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] :
( ( ~ defused(X0,X1)
& h(X0,X2)
& bomb(X0,X1) )
| ~ '$ki_exists_in_world_$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'('$ki_local_world',X0)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2] :
( ( ( h(X0,X2)
& bomb(X0,X1) )
=> defused(X0,X1) )
& '$ki_exists_in_world_$i'(X0,X2) ) ) ),
inference(rectify,[],[f8]) ).
tff(f8,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ? [X6] :
( ( ( h(X0,X6)
& bomb(X0,X2) )
=> defused(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X6) ) ) ),
inference(negated_conjecture,[],[f7]) ).
tff(f7,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ? [X6] :
( ( ( h(X0,X6)
& bomb(X0,X2) )
=> defused(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f39,plain,
! [X2: $i,X0: $i,X1: '$ki_world'] :
( ~ sP0(X0,X1,X2)
| ~ defused(X1,X0) ),
inference(cnf_transformation,[],[f25]) ).
tff(f25,plain,
! [X0,X1: '$ki_world',X2] :
( ( ~ defused(X1,X0)
& h(X1,X2)
& bomb(X1,X0) )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f24]) ).
tff(f24,plain,
! [X1,X0: '$ki_world',X2] :
( ( ~ defused(X0,X1)
& h(X0,X2)
& bomb(X0,X1) )
| ~ sP0(X1,X0,X2) ),
inference(nnf_transformation,[],[f22]) ).
tff(f73,plain,
defused(sK1,sK2),
inference(subsumption_resolution,[],[f69,f54]) ).
tff(f54,plain,
! [X0: $i] : h(sK1,X0),
inference(resolution,[],[f38,f52]) ).
tff(f38,plain,
! [X2: $i,X0: $i,X1: '$ki_world'] :
( ~ sP0(X0,X1,X2)
| h(X1,X2) ),
inference(cnf_transformation,[],[f25]) ).
tff(f69,plain,
! [X0: '$ki_world'] :
( ~ h(sK1,sK3(X0,sK2))
| defused(sK1,sK2) ),
inference(resolution,[],[f67,f53]) ).
tff(f53,plain,
bomb(sK1,sK2),
inference(resolution,[],[f37,f52]) ).
tff(f37,plain,
! [X2: $i,X0: $i,X1: '$ki_world'] :
( ~ sP0(X0,X1,X2)
| bomb(X1,X0) ),
inference(cnf_transformation,[],[f25]) ).
tff(f67,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ bomb(X3,X1)
| ~ h(X3,sK3(X0,X1))
| defused(X3,X1) ),
inference(subsumption_resolution,[],[f66,f48]) ).
tff(f48,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
tff(f66,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( defused(X3,X1)
| ~ h(X3,sK3(X0,X1))
| ~ bomb(X3,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f65,f49]) ).
tff(f65,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( defused(X3,X1)
| ~ h(X3,sK3(X0,X1))
| ~ bomb(X3,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f44,f48]) ).
tff(f44,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( defused(X3,X1)
| ~ h(X3,sK3(X0,X1))
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f30]) ).
tff(f30,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ( ! [X3: '$ki_world'] :
( defused(X3,X1)
| ~ h(X3,sK3(X0,X1))
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3) )
& '$ki_exists_in_world_$i'(X0,sK3(X0,X1)) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f18,f29]) ).
tff(f29,plain,
! [X0: '$ki_world',X1] :
( ? [X2] :
( ! [X3: '$ki_world'] :
( defused(X3,X1)
| ~ h(X3,X2)
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3) )
& '$ki_exists_in_world_$i'(X0,X2) )
=> ( ! [X3: '$ki_world'] :
( defused(X3,X1)
| ~ h(X3,sK3(X0,X1))
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3) )
& '$ki_exists_in_world_$i'(X0,sK3(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f18,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ? [X2] :
( ! [X3: '$ki_world'] :
( defused(X3,X1)
| ~ h(X3,X2)
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3) )
& '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f17]) ).
tff(f17,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ? [X2] :
( ! [X3: '$ki_world'] :
( defused(X3,X1)
| ~ h(X3,X2)
| ~ bomb(X3,X1)
| ~ '$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,[],[f10]) ).
tff(f10,plain,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2] :
( ! [X3: '$ki_world'] :
( '$ki_accessible'(X0,X3)
=> ( ( h(X3,X2)
& bomb(X3,X1) )
=> defused(X3,X1) ) )
& '$ki_exists_in_world_$i'(X0,X2) ) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ? [X6] :
( ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ( ( h(X5,X6)
& bomb(X5,X2) )
=> defused(X5,X2) ) )
& '$ki_exists_in_world_$i'(X0,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PLA053_5 : TPTP v8.2.0. Released v8.2.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat May 18 13:39:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.22/0.36 % (18650)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (18657)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.22/0.38 % (18657)First to succeed.
% 0.22/0.38 % (18657)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18650"
% 0.22/0.38 % (18654)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.38 % (18656)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.22/0.38 % (18657)Refutation found. Thanks to Tanya!
% 0.22/0.38 % SZS status Theorem for theBenchmark
% 0.22/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.38 % (18657)------------------------------
% 0.22/0.38 % (18657)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.38 % (18657)Termination reason: Refutation
% 0.22/0.38
% 0.22/0.38 % (18657)Memory used [KB]: 817
% 0.22/0.38 % (18657)Time elapsed: 0.004 s
% 0.22/0.38 % (18657)Instructions burned: 4 (million)
% 0.22/0.38 % (18650)Success in time 0.021 s
%------------------------------------------------------------------------------