TSTP Solution File: PLA053_2 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n028.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 : Mon May 22 15:41:23 EDT 2023
% Result : Theorem 0.18s 0.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 51 ( 11 unt; 11 typ; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 186 ( 69 ~; 54 |; 41 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 4 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' > $i ).
tff(func_def_2,type,
sK1: '$ki_world' ).
tff(func_def_4,type,
sK3: ( '$ki_world' * $i ) > $i ).
tff(func_def_6,type,
sK5: '$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(f68,plain,
$false,
inference(avatar_sat_refutation,[],[f56,f60,f67]) ).
tff(f67,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f66]) ).
tff(f66,plain,
( $false
| ~ spl6_1 ),
inference(subsumption_resolution,[],[f62,f44]) ).
tff(f44,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f62,plain,
( ~ '$ki_accessible'(sK1,sK1)
| ~ spl6_1 ),
inference(resolution,[],[f52,f36]) ).
tff(f36,plain,
'$ki_accessible'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f24]) ).
tff(f24,plain,
( '$ki_accessible'('$ki_local_world',sK1)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK1,X2)
| ( ~ defused(sK1,sK2)
& h(sK1,X2)
& bomb(sK1,sK2) ) )
& '$ki_exists_in_world_$i'(sK1,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f19,f23,f22]) ).
tff(f22,plain,
( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1] :
( ! [X2] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| ( ~ defused(X0,X1)
& h(X0,X2)
& bomb(X0,X1) ) )
& '$ki_exists_in_world_$i'(X0,X1) ) )
=> ( '$ki_accessible'('$ki_local_world',sK1)
& ? [X1] :
( ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK1,X2)
| ( ~ defused(sK1,X1)
& h(sK1,X2)
& bomb(sK1,X1) ) )
& '$ki_exists_in_world_$i'(sK1,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f23,plain,
( ? [X1] :
( ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK1,X2)
| ( ~ defused(sK1,X1)
& h(sK1,X2)
& bomb(sK1,X1) ) )
& '$ki_exists_in_world_$i'(sK1,X1) )
=> ( ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK1,X2)
| ( ~ defused(sK1,sK2)
& h(sK1,X2)
& bomb(sK1,sK2) ) )
& '$ki_exists_in_world_$i'(sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f19,plain,
? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1] :
( ! [X2] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| ( ~ defused(X0,X1)
& h(X0,X2)
& bomb(X0,X1) ) )
& '$ki_exists_in_world_$i'(X0,X1) ) ),
inference(flattening,[],[f18]) ).
tff(f18,plain,
? [X0: '$ki_world'] :
( ? [X1] :
( ! [X2] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| ( ~ defused(X0,X1)
& bomb(X0,X1)
& h(X0,X2) ) )
& '$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] :
( '$ki_exists_in_world_$i'(X0,X2)
& ( ( bomb(X0,X1)
& h(X0,X2) )
=> defused(X0,X1) ) ) ) ),
inference(rectify,[],[f8]) ).
tff(f8,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X5] :
( '$ki_exists_in_world_$i'(X0,X5)
& ( ( h(X0,X5)
& bomb(X0,X1) )
=> defused(X0,X1) ) ) ) ),
inference(negated_conjecture,[],[f7]) ).
tff(f7,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X5] :
( '$ki_exists_in_world_$i'(X0,X5)
& ( ( h(X0,X5)
& bomb(X0,X1) )
=> defused(X0,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f52,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK1) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f51]) ).
tff(f51,plain,
( spl6_1
<=> ! [X0: '$ki_world'] :
( ~ '$ki_accessible'(X0,sK1)
| ~ '$ki_accessible'('$ki_local_world',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
tff(f60,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f59]) ).
tff(f59,plain,
( $false
| ~ spl6_2 ),
inference(subsumption_resolution,[],[f57,f46]) ).
tff(f46,plain,
~ defused(sK1,sK2),
inference(subsumption_resolution,[],[f35,f43]) ).
tff(f43,plain,
! [X0: '$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(f35,plain,
! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK1,X2)
| ~ defused(sK1,sK2) ),
inference(cnf_transformation,[],[f24]) ).
tff(f57,plain,
( defused(sK1,sK2)
| ~ spl6_2 ),
inference(resolution,[],[f55,f47]) ).
tff(f47,plain,
bomb(sK1,sK2),
inference(subsumption_resolution,[],[f33,f43]) ).
tff(f33,plain,
! [X2: $i] :
( bomb(sK1,sK2)
| ~ '$ki_exists_in_world_$i'(sK1,X2) ),
inference(cnf_transformation,[],[f24]) ).
tff(f55,plain,
( ! [X1: $i] :
( ~ bomb(sK1,X1)
| defused(sK1,X1) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f54]) ).
tff(f54,plain,
( spl6_2
<=> ! [X1] :
( ~ bomb(sK1,X1)
| defused(sK1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
tff(f56,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f49,f54,f51]) ).
tff(f49,plain,
! [X0: '$ki_world',X1: $i] :
( ~ bomb(sK1,X1)
| ~ '$ki_accessible'(X0,sK1)
| defused(sK1,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f48,f43]) ).
tff(f48,plain,
! [X0: '$ki_world',X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ bomb(sK1,X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK1)
| defused(sK1,X1) ),
inference(resolution,[],[f45,f37]) ).
tff(f37,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ h(X3,sK3(X0,X1))
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ bomb(X3,X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| defused(X3,X1)
| ~ '$ki_accessible'(X0,X3) ),
inference(cnf_transformation,[],[f26]) ).
tff(f26,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ( '$ki_exists_in_world_$i'(X0,sK3(X0,X1))
& ! [X3: '$ki_world'] :
( ~ h(X3,sK3(X0,X1))
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3)
| defused(X3,X1) ) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f16,f25]) ).
tff(f25,plain,
! [X0: '$ki_world',X1] :
( ? [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
& ! [X3: '$ki_world'] :
( ~ h(X3,X2)
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3)
| defused(X3,X1) ) )
=> ( '$ki_exists_in_world_$i'(X0,sK3(X0,X1))
& ! [X3: '$ki_world'] :
( ~ h(X3,sK3(X0,X1))
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3)
| defused(X3,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f16,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ? [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
& ! [X3: '$ki_world'] :
( ~ h(X3,X2)
| ~ bomb(X3,X1)
| ~ '$ki_accessible'(X0,X3)
| defused(X3,X1) ) )
| ~ '$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] :
( '$ki_exists_in_world_$i'(X0,X5)
& ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ( ( bomb(X4,X1)
& h(X4,X5) )
=> defused(X4,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f45,plain,
! [X2: $i] : h(sK1,X2),
inference(subsumption_resolution,[],[f34,f43]) ).
tff(f34,plain,
! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK1,X2)
| h(sK1,X2) ),
inference(cnf_transformation,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% 0.03/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 22 12:39:22 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.49 % (14560)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.18/0.49 % (14568)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.18/0.50 % (14576)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.50 % (14560)First to succeed.
% 0.18/0.50 TRYING [1]
% 0.18/0.50 % (14560)Refutation found. Thanks to Tanya!
% 0.18/0.50 % SZS status Theorem for theBenchmark
% 0.18/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50 % (14560)------------------------------
% 0.18/0.50 % (14560)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50 % (14560)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50 % (14560)Termination reason: Refutation
% 0.18/0.50
% 0.18/0.50 % (14560)Memory used [KB]: 5884
% 0.18/0.50 % (14560)Time elapsed: 0.101 s
% 0.18/0.50 % (14560)Instructions burned: 1 (million)
% 0.18/0.50 % (14560)------------------------------
% 0.18/0.50 % (14560)------------------------------
% 0.18/0.50 % (14558)Success in time 0.162 s
%------------------------------------------------------------------------------