TSTP Solution File: PLA053_5 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---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_uns --cores 0 -t %d %s
% Computer : n002.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 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 45 ( 12 unt; 11 typ; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 164 ( 57 ~; 46 |; 41 &)
% ( 0 <=>; 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 : 7 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 78 (; 62 !; 16 ?; 47 :)
% 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' > $i ).
tff(func_def_5,type,
sK4: ( '$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(f69,plain,
$false,
inference(subsumption_resolution,[],[f66,f58]) ).
tff(f58,plain,
~ defused(sK0,sK1),
inference(subsumption_resolution,[],[f38,f48]) ).
tff(f48,plain,
! [X0: $i,X1: '$ki_world'] : '$ki_exists_in_world_$i'(X1,X0),
inference(cnf_transformation,[],[f12]) ).
tff(f12,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/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f38,plain,
! [X2: $i] :
( ~ defused(sK0,sK1)
| ~ '$ki_exists_in_world_$i'(sK0,X2) ),
inference(cnf_transformation,[],[f25]) ).
tff(f25,plain,
( '$ki_exists_in_world_$i'(sK0,sK1)
& ! [X2] :
( ( ~ defused(sK0,sK1)
& h(sK0,X2)
& bomb(sK0,sK1) )
| ~ '$ki_exists_in_world_$i'(sK0,X2) )
& '$ki_accessible'('$ki_local_world',sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f24,f23]) ).
tff(f23,plain,
( ? [X0: '$ki_world'] :
( ? [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2] :
( ( ~ defused(X0,X1)
& h(X0,X2)
& bomb(X0,X1) )
| ~ '$ki_exists_in_world_$i'(X0,X2) ) )
& '$ki_accessible'('$ki_local_world',X0) )
=> ( ? [X1] :
( '$ki_exists_in_world_$i'(sK0,X1)
& ! [X2] :
( ( ~ defused(sK0,X1)
& h(sK0,X2)
& bomb(sK0,X1) )
| ~ '$ki_exists_in_world_$i'(sK0,X2) ) )
& '$ki_accessible'('$ki_local_world',sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f24,plain,
( ? [X1] :
( '$ki_exists_in_world_$i'(sK0,X1)
& ! [X2] :
( ( ~ defused(sK0,X1)
& h(sK0,X2)
& bomb(sK0,X1) )
| ~ '$ki_exists_in_world_$i'(sK0,X2) ) )
=> ( '$ki_exists_in_world_$i'(sK0,sK1)
& ! [X2] :
( ( ~ defused(sK0,sK1)
& h(sK0,X2)
& bomb(sK0,sK1) )
| ~ '$ki_exists_in_world_$i'(sK0,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f19,plain,
? [X0: '$ki_world'] :
( ? [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2] :
( ( ~ defused(X0,X1)
& h(X0,X2)
& bomb(X0,X1) )
| ~ '$ki_exists_in_world_$i'(X0,X2) ) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f18]) ).
tff(f18,plain,
? [X0: '$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,[],[f13]) ).
tff(f13,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] :
( ( ( bomb(X0,X2)
& h(X0,X6) )
=> defused(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X6) ) ) ),
inference(negated_conjecture,[],[f7]) ).
tff(f7,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ? [X6] :
( ( ( bomb(X0,X2)
& h(X0,X6) )
=> defused(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f66,plain,
defused(sK0,sK1),
inference(resolution,[],[f64,f59]) ).
tff(f59,plain,
bomb(sK0,sK1),
inference(subsumption_resolution,[],[f36,f48]) ).
tff(f36,plain,
! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X2)
| bomb(sK0,sK1) ),
inference(cnf_transformation,[],[f25]) ).
tff(f64,plain,
! [X0: $i] :
( ~ bomb(sK0,X0)
| defused(sK0,X0) ),
inference(subsumption_resolution,[],[f63,f48]) ).
tff(f63,plain,
! [X0: $i,X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X1,X0)
| ~ bomb(sK0,X0)
| defused(sK0,X0) ),
inference(resolution,[],[f50,f57]) ).
tff(f57,plain,
! [X2: $i] : h(sK0,X2),
inference(subsumption_resolution,[],[f37,f48]) ).
tff(f37,plain,
! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X2)
| h(sK0,X2) ),
inference(cnf_transformation,[],[f25]) ).
tff(f50,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ h(X3,sK4(X0,X1))
| defused(X3,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ bomb(X3,X1) ),
inference(subsumption_resolution,[],[f49,f45]) ).
tff(f45,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(rectify,[],[f14]) ).
tff(f14,plain,
! [X1: '$ki_world',X0: '$ki_world'] : '$ki_accessible'(X1,X0),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X1: '$ki_world',X0: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
tff(f49,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ bomb(X3,X1)
| ~ h(X3,sK4(X0,X1))
| ~ '$ki_accessible'(X0,X3)
| defused(X3,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1) ),
inference(subsumption_resolution,[],[f44,f45]) ).
tff(f44,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ bomb(X3,X1)
| ~ h(X3,sK4(X0,X1))
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,X3)
| defused(X3,X1) ),
inference(cnf_transformation,[],[f31]) ).
tff(f31,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ( ! [X3: '$ki_world'] :
( ~ bomb(X3,X1)
| defused(X3,X1)
| ~ h(X3,sK4(X0,X1))
| ~ '$ki_accessible'(X0,X3) )
& '$ki_exists_in_world_$i'(X0,sK4(X0,X1)) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f22,f30]) ).
tff(f30,plain,
! [X0: '$ki_world',X1] :
( ? [X2] :
( ! [X3: '$ki_world'] :
( ~ bomb(X3,X1)
| defused(X3,X1)
| ~ h(X3,X2)
| ~ '$ki_accessible'(X0,X3) )
& '$ki_exists_in_world_$i'(X0,X2) )
=> ( ! [X3: '$ki_world'] :
( ~ bomb(X3,X1)
| defused(X3,X1)
| ~ h(X3,sK4(X0,X1))
| ~ '$ki_accessible'(X0,X3) )
& '$ki_exists_in_world_$i'(X0,sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f22,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ? [X2] :
( ! [X3: '$ki_world'] :
( ~ bomb(X3,X1)
| defused(X3,X1)
| ~ h(X3,X2)
| ~ '$ki_accessible'(X0,X3) )
& '$ki_exists_in_world_$i'(X0,X2) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f21]) ).
tff(f21,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ? [X2] :
( ! [X3: '$ki_world'] :
( defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,X2)
| ~ '$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'] :
( '$ki_accessible'(X0,X3)
=> ( ( bomb(X3,X1)
& h(X3,X2) )
=> defused(X3,X1) ) )
& '$ki_exists_in_world_$i'(X0,X2) ) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ? [X6] :
( '$ki_exists_in_world_$i'(X0,X6)
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ( ( bomb(X5,X2)
& h(X5,X6) )
=> defused(X5,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PLA053_5 : TPTP v8.2.0. Released v8.2.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 22 12:41:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.50 % (5119)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.50 % (5127)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.51 % (5135)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.20/0.51 % (5136)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.51 % (5127)First to succeed.
% 0.20/0.51 % (5127)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (5127)------------------------------
% 0.20/0.51 % (5127)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (5127)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (5127)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (5127)Memory used [KB]: 5884
% 0.20/0.51 % (5127)Time elapsed: 0.098 s
% 0.20/0.51 % (5127)Instructions burned: 2 (million)
% 0.20/0.51 % (5127)------------------------------
% 0.20/0.51 % (5127)------------------------------
% 0.20/0.51 % (5112)Success in time 0.163 s
%------------------------------------------------------------------------------