TSTP Solution File: PLA053_2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : PLA053_2 : 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 : n005.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 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 24
% Syntax : Number of formulae : 61 ( 10 unt; 11 typ; 0 def)
% Number of atoms : 205 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 218 ( 82 ~; 69 |; 41 &)
% ( 6 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 69 ( 53 !; 16 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_1,type,
sK0: '$ki_world' ).
tff(func_def_3,type,
sK2: ( '$ki_world' * $i ) > $i ).
tff(func_def_4,type,
sK3: '$ki_world' > $i ).
tff(func_def_5,type,
sK4: '$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(f88,plain,
$false,
inference(avatar_sat_refutation,[],[f52,f57,f64,f77,f81,f83,f87]) ).
tff(f87,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f84]) ).
tff(f84,plain,
( $false
| ~ spl6_1 ),
inference(resolution,[],[f47,f32]) ).
tff(f32,plain,
'$ki_exists_in_world_$i'(sK0,sK1),
inference(cnf_transformation,[],[f22]) ).
tff(f22,plain,
( ! [X2] :
( ( ~ defused(sK0,sK1)
& h(sK0,X2)
& bomb(sK0,sK1) )
| ~ '$ki_exists_in_world_$i'(sK0,X2) )
& '$ki_exists_in_world_$i'(sK0,sK1)
& '$ki_accessible'('$ki_local_world',sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f21,f20]) ).
tff(f20,plain,
( ? [X0: '$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) )
=> ( ? [X1] :
( ! [X2] :
( ( ~ defused(sK0,X1)
& h(sK0,X2)
& bomb(sK0,X1) )
| ~ '$ki_exists_in_world_$i'(sK0,X2) )
& '$ki_exists_in_world_$i'(sK0,X1) )
& '$ki_accessible'('$ki_local_world',sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f21,plain,
( ? [X1] :
( ! [X2] :
( ( ~ defused(sK0,X1)
& h(sK0,X2)
& bomb(sK0,X1) )
| ~ '$ki_exists_in_world_$i'(sK0,X2) )
& '$ki_exists_in_world_$i'(sK0,X1) )
=> ( ! [X2] :
( ( ~ defused(sK0,sK1)
& h(sK0,X2)
& bomb(sK0,sK1) )
| ~ '$ki_exists_in_world_$i'(sK0,X2) )
& '$ki_exists_in_world_$i'(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f14,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'('$ki_local_world',X0) ),
inference(flattening,[],[f13]) ).
tff(f13,plain,
? [X0: '$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)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X5] :
( ( ( h(X0,X5)
& bomb(X0,X1) )
=> defused(X0,X1) )
& '$ki_exists_in_world_$i'(X0,X5) ) ) ),
inference(negated_conjecture,[],[f7]) ).
tff(f7,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X5] :
( ( ( h(X0,X5)
& bomb(X0,X1) )
=> defused(X0,X1) )
& '$ki_exists_in_world_$i'(X0,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f47,plain,
( ! [X2: $i] : ~ '$ki_exists_in_world_$i'(sK0,X2)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f46]) ).
tff(f46,plain,
( spl6_1
<=> ! [X2] : ~ '$ki_exists_in_world_$i'(sK0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
tff(f83,plain,
spl6_6,
inference(avatar_contradiction_clause,[],[f82]) ).
tff(f82,plain,
( $false
| spl6_6 ),
inference(resolution,[],[f76,f36]) ).
tff(f36,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f76,plain,
( ~ '$ki_accessible'(sK0,sK0)
| spl6_6 ),
inference(avatar_component_clause,[],[f74]) ).
tff(f74,plain,
( spl6_6
<=> '$ki_accessible'(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).
tff(f81,plain,
spl6_5,
inference(avatar_contradiction_clause,[],[f78]) ).
tff(f78,plain,
( $false
| spl6_5 ),
inference(resolution,[],[f72,f32]) ).
tff(f72,plain,
( ~ '$ki_exists_in_world_$i'(sK0,sK1)
| spl6_5 ),
inference(avatar_component_clause,[],[f70]) ).
tff(f70,plain,
( spl6_5
<=> '$ki_exists_in_world_$i'(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
tff(f77,plain,
( ~ spl6_5
| ~ spl6_6
| ~ spl6_4 ),
inference(avatar_split_clause,[],[f65,f62,f74,f70]) ).
tff(f62,plain,
( spl6_4
<=> ! [X0: '$ki_world'] :
( ~ '$ki_accessible'(X0,sK0)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
tff(f65,plain,
( ~ '$ki_accessible'(sK0,sK0)
| ~ '$ki_exists_in_world_$i'(sK0,sK1)
| ~ spl6_4 ),
inference(resolution,[],[f63,f31]) ).
tff(f31,plain,
'$ki_accessible'('$ki_local_world',sK0),
inference(cnf_transformation,[],[f22]) ).
tff(f63,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK0)
| ~ '$ki_exists_in_world_$i'(X0,sK1) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f62]) ).
tff(f64,plain,
( ~ spl6_2
| spl6_4
| spl6_3 ),
inference(avatar_split_clause,[],[f60,f54,f62,f49]) ).
tff(f49,plain,
( spl6_2
<=> bomb(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
tff(f54,plain,
( spl6_3
<=> defused(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
tff(f60,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'(X0,sK0)
| ~ '$ki_exists_in_world_$i'(X0,sK1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ bomb(sK0,sK1) )
| spl6_3 ),
inference(resolution,[],[f59,f56]) ).
tff(f56,plain,
( ~ defused(sK0,sK1)
| spl6_3 ),
inference(avatar_component_clause,[],[f54]) ).
tff(f59,plain,
! [X0: $i,X1: '$ki_world'] :
( defused(sK0,X0)
| ~ '$ki_accessible'(X1,sK0)
| ~ '$ki_exists_in_world_$i'(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ bomb(sK0,X0) ),
inference(resolution,[],[f58,f42]) ).
tff(f42,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
! [X0: '$ki_world',X1] : '$ki_exists_in_world_$i'(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f58,plain,
! [X0: $i,X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(sK0,sK2(X1,X0))
| ~ bomb(sK0,X0)
| ~ '$ki_accessible'(X1,sK0)
| ~ '$ki_exists_in_world_$i'(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1)
| defused(sK0,X0) ),
inference(resolution,[],[f38,f34]) ).
tff(f34,plain,
! [X2: $i] :
( h(sK0,X2)
| ~ '$ki_exists_in_world_$i'(sK0,X2) ),
inference(cnf_transformation,[],[f22]) ).
tff(f38,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ h(X3,sK2(X0,X1))
| defused(X3,X1)
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f24]) ).
tff(f24,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ( ! [X3: '$ki_world'] :
( defused(X3,X1)
| ~ h(X3,sK2(X0,X1))
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3) )
& '$ki_exists_in_world_$i'(X0,sK2(X0,X1)) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f16,f23]) ).
tff(f23,plain,
! [X0: '$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: '$ki_world'] :
( defused(X3,X1)
| ~ h(X3,sK2(X0,X1))
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3) )
& '$ki_exists_in_world_$i'(X0,sK2(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f16,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'('$ki_local_world',X0) ),
inference(flattening,[],[f15]) ).
tff(f15,plain,
! [X0: '$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)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X5] :
( ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ( ( h(X4,X5)
& bomb(X4,X1) )
=> defused(X4,X1) ) )
& '$ki_exists_in_world_$i'(X0,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f57,plain,
( spl6_1
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f35,f54,f46]) ).
tff(f35,plain,
! [X2: $i] :
( ~ defused(sK0,sK1)
| ~ '$ki_exists_in_world_$i'(sK0,X2) ),
inference(cnf_transformation,[],[f22]) ).
tff(f52,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f33,f49,f46]) ).
tff(f33,plain,
! [X2: $i] :
( bomb(sK0,sK1)
| ~ '$ki_exists_in_world_$i'(sK0,X2) ),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.16 % Problem : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% 0.18/0.18 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.18/0.40 % Computer : n005.cluster.edu
% 0.18/0.40 % Model : x86_64 x86_64
% 0.18/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40 % Memory : 8042.1875MB
% 0.18/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40 % CPULimit : 300
% 0.18/0.40 % WCLimit : 300
% 0.18/0.40 % DateTime : Sat May 18 13:44:23 EDT 2024
% 0.18/0.41 % CPUTime :
% 0.18/0.41 % (12240)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.43 % (12247)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)
% 0.18/0.43 % (12241)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.18/0.43 % (12244)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.18/0.43 % (12243)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)
% 0.18/0.43 % (12242)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.18/0.43 Detected minimum model sizes of [1,1]
% 0.18/0.43 Detected maximum model sizes of [2,max]
% 0.18/0.43 TRYING [1,1]
% 0.18/0.43 Detected minimum model sizes of [1,1]
% 0.18/0.43 Detected maximum model sizes of [2,max]
% 0.18/0.43 TRYING [1,1]
% 0.18/0.43 TRYING [2,1]
% 0.18/0.43 Detected minimum model sizes of [1,1]
% 0.18/0.43 Detected maximum model sizes of [2,max]
% 0.18/0.43 TRYING [2,1]
% 0.18/0.43 TRYING [1,1]
% 0.18/0.43 TRYING [1,2]
% 0.18/0.43 TRYING [2,1]
% 0.18/0.43 TRYING [1,2]
% 0.18/0.43 TRYING [2,2]
% 0.18/0.43 Detected minimum model sizes of [1,1]
% 0.18/0.43 Detected maximum model sizes of [2,max]
% 0.18/0.43 TRYING [1,2]
% 0.18/0.43 TRYING [2,2]
% 0.18/0.43 TRYING [1,1]
% 0.18/0.43 % (12243)First to succeed.
% 0.18/0.43 TRYING [2,2]
% 0.18/0.43 TRYING [1,3]
% 0.18/0.43 TRYING [2,1]
% 0.18/0.43 TRYING [1,3]
% 0.18/0.43 TRYING [1,3]
% 0.18/0.43 TRYING [1,2]
% 0.18/0.43 TRYING [2,3]
% 0.18/0.43 TRYING [2,3]
% 0.18/0.43 TRYING [2,2]
% 0.18/0.43 TRYING [2,3]
% 0.18/0.43 % (12243)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-12240"
% 0.18/0.43 Cannot enumerate next child to try in an incomplete setup
% 0.18/0.43 % (12241)Refutation not found, incomplete strategy% (12241)------------------------------
% 0.18/0.43 % (12241)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.43 % (12241)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.43
% 0.18/0.43 % (12241)Memory used [KB]: 732
% 0.18/0.43 % (12241)Time elapsed: 0.006 s
% 0.18/0.43 % (12241)Instructions burned: 7 (million)
% 0.18/0.43 TRYING [1,4]
% 0.18/0.43 TRYING [1,3]
% 0.18/0.43 Cannot enumerate next child to try in an incomplete setup
% 0.18/0.43 % (12244)Refutation not found, incomplete strategy% (12244)------------------------------
% 0.18/0.43 % (12244)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.43 % (12244)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.43
% 0.18/0.43 % (12244)Memory used [KB]: 805
% 0.18/0.43 % (12244)Time elapsed: 0.005 s
% 0.18/0.43 % (12244)Instructions burned: 8 (million)
% 0.18/0.43 % (12241)------------------------------
% 0.18/0.43 % (12241)------------------------------
% 0.18/0.43 TRYING [2,3]
% 0.18/0.43 TRYING [2,4]
% 0.18/0.43 % (12244)------------------------------
% 0.18/0.43 % (12244)------------------------------
% 0.18/0.43 % (12243)Refutation found. Thanks to Tanya!
% 0.18/0.43 % SZS status Theorem for theBenchmark
% 0.18/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.43 % (12243)------------------------------
% 0.18/0.43 % (12243)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.43 % (12243)Termination reason: Refutation
% 0.18/0.43
% 0.18/0.43 % (12243)Memory used [KB]: 842
% 0.18/0.43 % (12243)Time elapsed: 0.006 s
% 0.18/0.43 % (12243)Instructions burned: 5 (million)
% 0.18/0.43 % (12240)Success in time 0.012 s
%------------------------------------------------------------------------------