TSTP Solution File: PLA053_5 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : PLA053_5 : 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 : n013.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 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 57 ( 10 unt; 11 typ; 0 def)
% Number of atoms : 240 ( 0 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 275 ( 105 ~; 91 |; 50 &)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 126 (; 105 !; 21 ?; 83 :)
% 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' > $i ).
tff(func_def_4,type,
sK3: ( '$ki_world' * $i ) > $i ).
tff(func_def_5,type,
sK4: '$ki_world' ).
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(f66,plain,
$false,
inference(subsumption_resolution,[],[f65,f41]) ).
tff(f41,plain,
! [X0: $i,X1: '$ki_world'] : '$ki_exists_in_world_$i'(X1,X0),
inference(cnf_transformation,[],[f10]) ).
tff(f10,plain,
! [X0,X1: '$ki_world'] : '$ki_exists_in_world_$i'(X1,X0),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X2,X0: '$ki_world'] : '$ki_exists_in_world_$i'(X0,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f65,plain,
! [X0: '$ki_world'] : ~ '$ki_exists_in_world_$i'(sK4,sK3(X0,sK5)),
inference(resolution,[],[f64,f42]) ).
tff(f42,plain,
! [X2: $i] :
( h(sK4,X2)
| ~ '$ki_exists_in_world_$i'(sK4,X2) ),
inference(cnf_transformation,[],[f33]) ).
tff(f33,plain,
( '$ki_accessible'('$ki_local_world',sK4)
& '$ki_exists_in_world_$i'(sK4,sK5)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK4,X2)
| ( bomb(sK4,sK5)
& ~ defused(sK4,sK5)
& h(sK4,X2) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f17,f32,f31]) ).
tff(f31,plain,
( ? [X0: '$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)
& ~ defused(X0,X1)
& h(X0,X2) ) ) ) )
=> ( '$ki_accessible'('$ki_local_world',sK4)
& ? [X1] :
( '$ki_exists_in_world_$i'(sK4,X1)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK4,X2)
| ( bomb(sK4,X1)
& ~ defused(sK4,X1)
& h(sK4,X2) ) ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f32,plain,
( ? [X1] :
( '$ki_exists_in_world_$i'(sK4,X1)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK4,X2)
| ( bomb(sK4,X1)
& ~ defused(sK4,X1)
& h(sK4,X2) ) ) )
=> ( '$ki_exists_in_world_$i'(sK4,sK5)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK4,X2)
| ( bomb(sK4,sK5)
& ~ defused(sK4,sK5)
& h(sK4,X2) ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f17,plain,
? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| ( bomb(X0,X1)
& ~ defused(X0,X1)
& h(X0,X2) ) ) ) ),
inference(flattening,[],[f16]) ).
tff(f16,plain,
? [X0: '$ki_world'] :
( ? [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',X0) ),
inference(ennf_transformation,[],[f14]) ).
tff(f14,plain,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
& ( ( h(X0,X2)
& bomb(X0,X1) )
=> defused(X0,X1) ) ) ) ),
inference(rectify,[],[f8]) ).
tff(f8,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ? [X6] :
( '$ki_exists_in_world_$i'(X0,X6)
& ( ( h(X0,X6)
& bomb(X0,X2) )
=> defused(X0,X2) ) ) ) ),
inference(negated_conjecture,[],[f7]) ).
tff(f7,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ? [X6] :
( '$ki_exists_in_world_$i'(X0,X6)
& ( ( h(X0,X6)
& bomb(X0,X2) )
=> defused(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f64,plain,
! [X0: '$ki_world'] : ~ h(sK4,sK3(X0,sK5)),
inference(subsumption_resolution,[],[f63,f41]) ).
tff(f63,plain,
! [X0: '$ki_world',X1: $i] :
( ~ '$ki_exists_in_world_$i'(sK4,X1)
| ~ h(sK4,sK3(X0,sK5)) ),
inference(subsumption_resolution,[],[f62,f56]) ).
tff(f56,plain,
! [X0: '$ki_world'] : bomb(X0,sK5),
inference(subsumption_resolution,[],[f54,f41]) ).
tff(f54,plain,
! [X0: '$ki_world',X1: $i] :
( bomb(X0,sK5)
| ~ '$ki_exists_in_world_$i'(sK4,X1) ),
inference(resolution,[],[f53,f44]) ).
tff(f44,plain,
! [X2: $i] :
( bomb(sK4,sK5)
| ~ '$ki_exists_in_world_$i'(sK4,X2) ),
inference(cnf_transformation,[],[f33]) ).
tff(f53,plain,
! [X0: '$ki_world',X1: $i] :
( ~ bomb(sK4,X1)
| bomb(X0,X1) ),
inference(subsumption_resolution,[],[f52,f41]) ).
tff(f52,plain,
! [X0: '$ki_world',X1: $i] :
( ~ bomb(sK4,X1)
| ~ '$ki_exists_in_world_$i'(sK4,sK2)
| bomb(X0,X1) ),
inference(resolution,[],[f51,f42]) ).
tff(f51,plain,
! [X2: $i,X3: '$ki_world',X1: '$ki_world'] :
( ~ h(X1,sK2)
| bomb(X3,X2)
| ~ bomb(X1,X2) ),
inference(subsumption_resolution,[],[f50,f47]) ).
tff(f47,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X1,X0),
inference(cnf_transformation,[],[f12]) ).
tff(f12,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X1,X0),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X1: '$ki_world',X0: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
tff(f50,plain,
! [X2: $i,X3: '$ki_world',X1: '$ki_world'] :
( bomb(X3,X2)
| ~ '$ki_accessible'(X1,X3)
| ~ h(X1,sK2)
| ~ bomb(X1,X2) ),
inference(subsumption_resolution,[],[f49,f47]) ).
tff(f49,plain,
! [X2: $i,X3: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ bomb(X1,X2)
| ~ h(X1,sK2)
| ~ '$ki_accessible'(X1,X3)
| bomb(X3,X2) ),
inference(subsumption_resolution,[],[f38,f41]) ).
tff(f38,plain,
! [X2: $i,X3: '$ki_world',X1: '$ki_world'] :
( ~ bomb(X1,X2)
| ~ '$ki_exists_in_world_$i'(X1,X2)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,X3)
| bomb(X3,X2)
| ~ h(X1,sK2) ),
inference(cnf_transformation,[],[f28]) ).
tff(f28,plain,
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ! [X2] :
( ! [X3: '$ki_world'] :
( bomb(X3,X2)
| ~ '$ki_accessible'(X1,X3) )
| ~ h(X1,sK2)
| ~ '$ki_exists_in_world_$i'(X1,X2)
| ~ bomb(X1,X2) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f22,f27]) ).
tff(f27,plain,
( ? [X0] :
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ! [X2] :
( ! [X3: '$ki_world'] :
( bomb(X3,X2)
| ~ '$ki_accessible'(X1,X3) )
| ~ h(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,X2)
| ~ bomb(X1,X2) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',X0) )
=> ( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ! [X2] :
( ! [X3: '$ki_world'] :
( bomb(X3,X2)
| ~ '$ki_accessible'(X1,X3) )
| ~ h(X1,sK2)
| ~ '$ki_exists_in_world_$i'(X1,X2)
| ~ bomb(X1,X2) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f22,plain,
? [X0] :
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ! [X2] :
( ! [X3: '$ki_world'] :
( bomb(X3,X2)
| ~ '$ki_accessible'(X1,X3) )
| ~ h(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,X2)
| ~ bomb(X1,X2) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
inference(flattening,[],[f21]) ).
tff(f21,plain,
? [X0] :
( ! [X1: '$ki_world'] :
( ! [X2] :
( ! [X3: '$ki_world'] :
( bomb(X3,X2)
| ~ '$ki_accessible'(X1,X3) )
| ~ bomb(X1,X2)
| ~ h(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,X2) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
& '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f15]) ).
tff(f15,plain,
? [X0] :
( ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X1,X2)
=> ( ( bomb(X1,X2)
& h(X1,X0) )
=> ! [X3: '$ki_world'] :
( '$ki_accessible'(X1,X3)
=> bomb(X3,X2) ) ) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
? [X4] :
( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ( ( h(X0,X4)
& bomb(X0,X2) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> bomb(X5,X2) ) ) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f62,plain,
! [X0: '$ki_world',X1: $i] :
( ~ bomb(sK4,sK5)
| ~ '$ki_exists_in_world_$i'(sK4,X1)
| ~ h(sK4,sK3(X0,sK5)) ),
inference(resolution,[],[f61,f43]) ).
tff(f43,plain,
! [X2: $i] :
( ~ defused(sK4,sK5)
| ~ '$ki_exists_in_world_$i'(sK4,X2) ),
inference(cnf_transformation,[],[f33]) ).
tff(f61,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( defused(X3,X1)
| ~ h(X3,sK3(X0,X1))
| ~ bomb(X3,X1) ),
inference(subsumption_resolution,[],[f60,f47]) ).
tff(f60,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,sK3(X0,X1))
| ~ '$ki_accessible'(X0,X3) ),
inference(subsumption_resolution,[],[f59,f41]) ).
tff(f59,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( defused(X3,X1)
| ~ bomb(X3,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'(X0,X3)
| ~ h(X3,sK3(X0,X1)) ),
inference(subsumption_resolution,[],[f40,f47]) ).
tff(f40,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ~ h(X3,sK3(X0,X1))
| ~ bomb(X3,X1)
| defused(X3,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'(X0,X3) ),
inference(cnf_transformation,[],[f30]) ).
tff(f30,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ( ! [X3: '$ki_world'] :
( ~ '$ki_accessible'(X0,X3)
| defused(X3,X1)
| ~ h(X3,sK3(X0,X1))
| ~ bomb(X3,X1) )
& '$ki_exists_in_world_$i'(X0,sK3(X0,X1)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f20,f29]) ).
tff(f29,plain,
! [X0: '$ki_world',X1] :
( ? [X2] :
( ! [X3: '$ki_world'] :
( ~ '$ki_accessible'(X0,X3)
| defused(X3,X1)
| ~ h(X3,X2)
| ~ bomb(X3,X1) )
& '$ki_exists_in_world_$i'(X0,X2) )
=> ( ! [X3: '$ki_world'] :
( ~ '$ki_accessible'(X0,X3)
| defused(X3,X1)
| ~ h(X3,sK3(X0,X1))
| ~ bomb(X3,X1) )
& '$ki_exists_in_world_$i'(X0,sK3(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f20,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ? [X2] :
( ! [X3: '$ki_world'] :
( ~ '$ki_accessible'(X0,X3)
| defused(X3,X1)
| ~ h(X3,X2)
| ~ bomb(X3,X1) )
& '$ki_exists_in_world_$i'(X0,X2) ) ) ),
inference(flattening,[],[f19]) ).
tff(f19,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ? [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
& ! [X3: '$ki_world'] :
( defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,X2)
| ~ '$ki_accessible'(X0,X3) ) )
| ~ '$ki_exists_in_world_$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_$i'(X0,X1)
=> ? [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
& ! [X3: '$ki_world'] :
( '$ki_accessible'(X0,X3)
=> ( ( bomb(X3,X1)
& h(X3,X2) )
=> defused(X3,X1) ) ) ) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: '$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/sandbox2/benchmark/theBenchmark.p',ax3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PLA053_5 : 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_sat --cores 0 -t %d %s
% 0.14/0.33 % Computer : n013.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 22 12:22:05 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.19/0.48 % (14462)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)
% 0.19/0.48 % (14454)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.49 % (14462)First to succeed.
% 0.19/0.49 % (14446)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.49 % (14462)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (14462)------------------------------
% 0.19/0.49 % (14462)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49 % (14462)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49 % (14462)Termination reason: Refutation
% 0.19/0.49
% 0.19/0.49 % (14462)Memory used [KB]: 895
% 0.19/0.49 % (14462)Time elapsed: 0.058 s
% 0.19/0.49 % (14462)Instructions burned: 2 (million)
% 0.19/0.49 % (14462)------------------------------
% 0.19/0.49 % (14462)------------------------------
% 0.19/0.49 % (14439)Success in time 0.149 s
%------------------------------------------------------------------------------