TSTP Solution File: PLA053_4 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : PLA053_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 : n009.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 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 23
% Syntax : Number of formulae : 60 ( 10 unt; 11 typ; 0 def)
% Number of atoms : 193 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 210 ( 79 ~; 65 |; 41 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 13 ( 13 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 58 !; 16 ?; 41 :)
% 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(f92,plain,
$false,
inference(avatar_sat_refutation,[],[f58,f63,f80,f86,f89,f91]) ).
tff(f91,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f90]) ).
tff(f90,plain,
( $false
| ~ spl6_1 ),
inference(subsumption_resolution,[],[f53,f47]) ).
tff(f47,plain,
! [X0: '$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(f53,plain,
( ! [X2: $i] : ~ '$ki_exists_in_world_$i'(sK0,X2)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f52]) ).
tff(f52,plain,
( spl6_1
<=> ! [X2] : ~ '$ki_exists_in_world_$i'(sK0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
tff(f89,plain,
( spl6_2
| ~ spl6_3
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f88]) ).
tff(f88,plain,
( $false
| spl6_2
| ~ spl6_3
| ~ spl6_5 ),
inference(subsumption_resolution,[],[f87,f62]) ).
tff(f62,plain,
( bomb(sK0,sK1)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f60]) ).
tff(f60,plain,
( spl6_3
<=> bomb(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
tff(f87,plain,
( ~ bomb(sK0,sK1)
| spl6_2
| ~ spl6_5 ),
inference(resolution,[],[f79,f57]) ).
tff(f57,plain,
( ~ defused(sK0,sK1)
| spl6_2 ),
inference(avatar_component_clause,[],[f55]) ).
tff(f55,plain,
( spl6_2
<=> defused(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
tff(f79,plain,
( ! [X0: $i] :
( defused(sK0,X0)
| ~ bomb(sK0,X0) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f78]) ).
tff(f78,plain,
( spl6_5
<=> ! [X0] :
( defused(sK0,X0)
| ~ bomb(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
tff(f86,plain,
~ spl6_4,
inference(avatar_contradiction_clause,[],[f85]) ).
tff(f85,plain,
( $false
| ~ spl6_4 ),
inference(subsumption_resolution,[],[f82,f36]) ).
tff(f36,plain,
'$ki_accessible'('$ki_local_world',sK0),
inference(cnf_transformation,[],[f27]) ).
tff(f27,plain,
( ! [X2] :
( ( ~ defused(sK0,sK1)
& h(sK0,X2)
& bomb(sK0,sK1) )
| ~ '$ki_exists_in_world_$i'(sK0,X2) )
& '$ki_exists_in_world_$i'(sK0,sK1)
& '$ki_accessible'('$ki_local_world',sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f26,f25]) ).
tff(f25,plain,
( ? [X0: '$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(f26,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(f17,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'('$ki_local_world',X0) ),
inference(flattening,[],[f16]) ).
tff(f16,plain,
? [X0: '$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(ennf_transformation,[],[f10]) ).
tff(f10,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_$i'(X0,X2) ) ) ),
inference(rectify,[],[f9]) ).
tff(f9,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ? [X7] :
( ( ( h(X0,X7)
& bomb(X0,X3) )
=> defused(X0,X3) )
& '$ki_exists_in_world_$i'(X0,X7) ) ) ),
inference(negated_conjecture,[],[f8]) ).
tff(f8,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ? [X7] :
( ( ( h(X0,X7)
& bomb(X0,X3) )
=> defused(X0,X3) )
& '$ki_exists_in_world_$i'(X0,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f82,plain,
( ~ '$ki_accessible'('$ki_local_world',sK0)
| ~ spl6_4 ),
inference(resolution,[],[f76,f41]) ).
tff(f41,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f76,plain,
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,sK0) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f75]) ).
tff(f75,plain,
( spl6_4
<=> ! [X1: '$ki_world'] :
( ~ '$ki_accessible'(X1,sK0)
| ~ '$ki_accessible'('$ki_local_world',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
tff(f80,plain,
( spl6_4
| spl6_5 ),
inference(avatar_split_clause,[],[f73,f78,f75]) ).
tff(f73,plain,
! [X0: $i,X1: '$ki_world'] :
( defused(sK0,X0)
| ~ bomb(sK0,X0)
| ~ '$ki_accessible'(X1,sK0)
| ~ '$ki_accessible'('$ki_local_world',X1) ),
inference(resolution,[],[f72,f64]) ).
tff(f64,plain,
! [X2: $i] : h(sK0,X2),
inference(subsumption_resolution,[],[f39,f47]) ).
tff(f39,plain,
! [X2: $i] :
( h(sK0,X2)
| ~ '$ki_exists_in_world_$i'(sK0,X2) ),
inference(cnf_transformation,[],[f27]) ).
tff(f72,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ h(X3,sK2(X0,X1))
| defused(X3,X1)
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f43,f47]) ).
tff(f43,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( defused(X3,X1)
| ~ h(X3,sK2(X0,X1))
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f29]) ).
tff(f29,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'('$ki_local_world',X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f19,f28]) ).
tff(f28,plain,
! [X0: '$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(f19,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'('$ki_local_world',X0) ),
inference(flattening,[],[f18]) ).
tff(f18,plain,
! [X0: '$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(ennf_transformation,[],[f11]) ).
tff(f11,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_$i'(X0,X2) ) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ? [X7] :
( ! [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
=> ( ( h(X6,X7)
& bomb(X6,X3) )
=> defused(X6,X3) ) )
& '$ki_exists_in_world_$i'(X0,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f63,plain,
( spl6_1
| spl6_3 ),
inference(avatar_split_clause,[],[f38,f60,f52]) ).
tff(f38,plain,
! [X2: $i] :
( bomb(sK0,sK1)
| ~ '$ki_exists_in_world_$i'(sK0,X2) ),
inference(cnf_transformation,[],[f27]) ).
tff(f58,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f40,f55,f52]) ).
tff(f40,plain,
! [X2: $i] :
( ~ defused(sK0,sK1)
| ~ '$ki_exists_in_world_$i'(sK0,X2) ),
inference(cnf_transformation,[],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : PLA053_4 : TPTP v8.2.0. Released v8.2.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 13:33:07 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (1112)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (1116)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.39 Detected minimum model sizes of [1,1]
% 0.14/0.39 Detected maximum model sizes of [2,max]
% 0.14/0.39 TRYING [1,1]
% 0.14/0.39 TRYING [2,1]
% 0.14/0.39 % (1114)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39 TRYING [1,2]
% 0.14/0.39 % (1119)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)
% 0.14/0.39 TRYING [2,2]
% 0.14/0.39 TRYING [1,3]
% 0.14/0.39 TRYING [2,3]
% 0.14/0.39 Detected minimum model sizes of [1,1]
% 0.14/0.39 Detected maximum model sizes of [2,max]
% 0.14/0.39 TRYING [1,1]
% 0.14/0.39 TRYING [2,1]
% 0.14/0.39 % (1113)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.39 Cannot enumerate next child to try in an incomplete setup
% 0.14/0.39 % (1116)Refutation not found, incomplete strategy% (1116)------------------------------
% 0.14/0.39 % (1116)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (1116)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.39
% 0.14/0.39 % (1116)Memory used [KB]: 806
% 0.14/0.39 % (1116)Time elapsed: 0.007 s
% 0.14/0.39 % (1116)Instructions burned: 8 (million)
% 0.14/0.39 TRYING [1,2]
% 0.14/0.39 TRYING [2,2]
% 0.14/0.39 Detected minimum model sizes of [1,1]
% 0.14/0.39 Detected maximum model sizes of [2,max]
% 0.14/0.39 % (1116)------------------------------
% 0.14/0.39 % (1116)------------------------------
% 0.14/0.39 TRYING [1,1]
% 0.14/0.39 TRYING [1,3]
% 0.14/0.39 Detected minimum model sizes of [1,1]
% 0.14/0.39 Detected maximum model sizes of [2,max]
% 0.14/0.39 TRYING [1,1]
% 0.14/0.39 TRYING [2,1]
% 0.14/0.39 TRYING [2,3]
% 0.14/0.39 TRYING [1,2]
% 0.14/0.39 TRYING [2,2]
% 0.14/0.39 Cannot enumerate next child to try in an incomplete setup
% 0.14/0.39 % (1114)Refutation not found, incomplete strategy% (1114)------------------------------
% 0.14/0.39 % (1114)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (1114)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.39
% 0.14/0.39 % (1114)Memory used [KB]: 806
% 0.14/0.39 % (1114)Time elapsed: 0.006 s
% 0.14/0.39 % (1114)Instructions burned: 8 (million)
% 0.14/0.39 TRYING [1,3]
% 0.14/0.39 % (1114)------------------------------
% 0.14/0.39 % (1114)------------------------------
% 0.14/0.40 TRYING [2,3]
% 0.14/0.40 % (1118)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.40 Cannot enumerate next child to try in an incomplete setup
% 0.14/0.40 % (1113)Refutation not found, incomplete strategy% (1113)------------------------------
% 0.14/0.40 % (1113)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40 % (1113)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.40
% 0.14/0.40 % (1113)Memory used [KB]: 796
% 0.14/0.40 % (1113)Time elapsed: 0.004 s
% 0.14/0.40 % (1113)Instructions burned: 7 (million)
% 0.14/0.40 % (1113)------------------------------
% 0.14/0.40 % (1113)------------------------------
% 0.14/0.40 TRYING [2,1]
% 0.14/0.40 TRYING [1,2]
% 0.14/0.40 TRYING [2,2]
% 0.14/0.40 % (1118)First to succeed.
% 0.14/0.40 TRYING [1,3]
% 0.14/0.40 TRYING [2,3]
% 0.14/0.40 % (1115)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)
% 0.14/0.40 % (1118)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1112"
% 0.14/0.40 TRYING [1,4]
% 0.14/0.40 TRYING [2,4]
% 0.14/0.40 % (1118)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40 % (1118)------------------------------
% 0.14/0.40 % (1118)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40 % (1118)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (1118)Memory used [KB]: 837
% 0.14/0.40 % (1118)Time elapsed: 0.005 s
% 0.14/0.40 % (1118)Instructions burned: 5 (million)
% 0.14/0.40 % (1112)Success in time 0.037 s
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