TSTP Solution File: PLA053_2 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---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_sat --cores 0 -t %d %s
% Computer : n021.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 15:41:24 EDT 2023
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 44 ( 9 unt; 11 typ; 0 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 181 ( 69 ~; 51 |; 41 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 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 : 7 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 67 (; 51 !; 16 ?; 36 :)
% 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' > $i ).
tff(func_def_3,type,
sK2: '$ki_world' ).
tff(func_def_5,type,
sK4: ( '$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(f76,plain,
$false,
inference(resolution,[],[f74,f34]) ).
tff(f34,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f74,plain,
~ '$ki_accessible'(sK2,sK2),
inference(resolution,[],[f62,f45]) ).
tff(f45,plain,
! [X0: $i,X1: '$ki_world'] : '$ki_exists_in_world_$i'(X1,X0),
inference(cnf_transformation,[],[f13]) ).
tff(f13,plain,
! [X0,X1: '$ki_world'] : '$ki_exists_in_world_$i'(X1,X0),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X1,X0: '$ki_world'] : '$ki_exists_in_world_$i'(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f62,plain,
! [X0: $i] :
( ~ '$ki_exists_in_world_$i'(sK2,X0)
| ~ '$ki_accessible'(sK2,sK2) ),
inference(resolution,[],[f54,f39]) ).
tff(f39,plain,
! [X2: $i] :
( bomb(sK2,sK3)
| ~ '$ki_exists_in_world_$i'(sK2,X2) ),
inference(cnf_transformation,[],[f27]) ).
tff(f27,plain,
( '$ki_accessible'('$ki_local_world',sK2)
& '$ki_exists_in_world_$i'(sK2,sK3)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK2,X2)
| ( bomb(sK2,sK3)
& h(sK2,X2)
& ~ defused(sK2,sK3) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f19,f26,f25]) ).
tff(f25,plain,
( ? [X0: '$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) ) ) ) )
=> ( '$ki_accessible'('$ki_local_world',sK2)
& ? [X1] :
( '$ki_exists_in_world_$i'(sK2,X1)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK2,X2)
| ( bomb(sK2,X1)
& h(sK2,X2)
& ~ defused(sK2,X1) ) ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f26,plain,
( ? [X1] :
( '$ki_exists_in_world_$i'(sK2,X1)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK2,X2)
| ( bomb(sK2,X1)
& h(sK2,X2)
& ~ defused(sK2,X1) ) ) )
=> ( '$ki_exists_in_world_$i'(sK2,sK3)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK2,X2)
| ( bomb(sK2,sK3)
& h(sK2,X2)
& ~ defused(sK2,sK3) ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f19,plain,
? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| ( bomb(X0,X1)
& h(X0,X2)
& ~ defused(X0,X1) ) ) ) ),
inference(flattening,[],[f18]) ).
tff(f18,plain,
? [X0: '$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,[],[f11]) ).
tff(f11,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] :
( '$ki_exists_in_world_$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_$i'(X0,X5)
& ( ( h(X0,X5)
& bomb(X0,X1) )
=> defused(X0,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f54,plain,
( ~ bomb(sK2,sK3)
| ~ '$ki_accessible'(sK2,sK2) ),
inference(resolution,[],[f53,f41]) ).
tff(f41,plain,
'$ki_accessible'('$ki_local_world',sK2),
inference(cnf_transformation,[],[f27]) ).
tff(f53,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ~ bomb(sK2,sK3)
| ~ '$ki_accessible'(X0,sK2) ),
inference(resolution,[],[f51,f45]) ).
tff(f51,plain,
! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ '$ki_accessible'(X0,sK2)
| ~ bomb(sK2,sK3)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(resolution,[],[f49,f45]) ).
tff(f49,plain,
! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(sK2,sK4(X0,sK3))
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ bomb(sK2,sK3)
| ~ '$ki_accessible'(X0,sK2) ),
inference(resolution,[],[f48,f38]) ).
tff(f38,plain,
! [X2: $i] :
( h(sK2,X2)
| ~ '$ki_exists_in_world_$i'(sK2,X2) ),
inference(cnf_transformation,[],[f27]) ).
tff(f48,plain,
! [X0: '$ki_world'] :
( ~ h(sK2,sK4(X0,sK3))
| ~ '$ki_exists_in_world_$i'(X0,sK3)
| ~ bomb(sK2,sK3)
| ~ '$ki_accessible'(X0,sK2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(resolution,[],[f43,f46]) ).
tff(f46,plain,
~ defused(sK2,sK3),
inference(resolution,[],[f45,f37]) ).
tff(f37,plain,
! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK2,X2)
| ~ defused(sK2,sK3) ),
inference(cnf_transformation,[],[f27]) ).
tff(f43,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( defused(X3,X1)
| ~ bomb(X3,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ h(X3,sK4(X0,X1))
| ~ '$ki_accessible'(X0,X3)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f29]) ).
tff(f29,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ( ! [X3: '$ki_world'] :
( ~ '$ki_accessible'(X0,X3)
| ~ h(X3,sK4(X0,X1))
| ~ bomb(X3,X1)
| defused(X3,X1) )
& '$ki_exists_in_world_$i'(X0,sK4(X0,X1)) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f17,f28]) ).
tff(f28,plain,
! [X0: '$ki_world',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) )
=> ( ! [X3: '$ki_world'] :
( ~ '$ki_accessible'(X0,X3)
| ~ h(X3,sK4(X0,X1))
| ~ bomb(X3,X1)
| defused(X3,X1) )
& '$ki_exists_in_world_$i'(X0,sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f17,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ? [X2] :
( ! [X3: '$ki_world'] :
( ~ '$ki_accessible'(X0,X3)
| ~ h(X3,X2)
| ~ bomb(X3,X1)
| defused(X3,X1) )
& '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f16]) ).
tff(f16,plain,
! [X0: '$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(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)
=> ( ( bomb(X4,X1)
& h(X4,X5) )
=> defused(X4,X1) ) )
& '$ki_exists_in_world_$i'(X0,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 22 12:25:15 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.51 % (19987)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.51 % (19995)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.51 % (19979)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51 % (19979)First to succeed.
% 0.19/0.51 % (19992)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.51 % (19979)Refutation found. Thanks to Tanya!
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51 % (19979)------------------------------
% 0.19/0.51 % (19979)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (19979)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (19979)Termination reason: Refutation
% 0.19/0.51
% 0.19/0.51 % (19979)Memory used [KB]: 895
% 0.19/0.51 % (19979)Time elapsed: 0.104 s
% 0.19/0.51 % (19979)Instructions burned: 3 (million)
% 0.19/0.51 % (19979)------------------------------
% 0.19/0.51 % (19979)------------------------------
% 0.19/0.51 % (19969)Success in time 0.155 s
%------------------------------------------------------------------------------