TSTP Solution File: PLA053_4 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : PLA053_4 : 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 : n008.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 1.18s 0.64s
% Output : Refutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% 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 : 166 ( 59 ~; 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 : 71 (; 55 !; 16 ?; 39 :)
% 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 ) > $i ).
tff(func_def_3,type,
sK2: '$ki_world' ).
tff(func_def_5,type,
sK4: '$ki_world' > $i ).
tff(func_def_6,type,
sK5: '$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(f66,plain,
$false,
inference(subsumption_resolution,[],[f65,f47]) ).
tff(f47,plain,
'$ki_accessible'('$ki_local_world',sK2),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
( '$ki_accessible'('$ki_local_world',sK2)
& '$ki_exists_in_world_$i'(sK2,sK3)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK2,X2)
| ( bomb(sK2,sK3)
& ~ defused(sK2,sK3)
& h(sK2,X2) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f25,f31,f30]) ).
tff(f30,plain,
( ? [X0: '$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',sK2)
& ? [X1] :
( '$ki_exists_in_world_$i'(sK2,X1)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK2,X2)
| ( bomb(sK2,X1)
& ~ defused(sK2,X1)
& h(sK2,X2) ) ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f31,plain,
( ? [X1] :
( '$ki_exists_in_world_$i'(sK2,X1)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK2,X2)
| ( bomb(sK2,X1)
& ~ defused(sK2,X1)
& h(sK2,X2) ) ) )
=> ( '$ki_exists_in_world_$i'(sK2,sK3)
& ! [X2] :
( ~ '$ki_exists_in_world_$i'(sK2,X2)
| ( bomb(sK2,sK3)
& ~ defused(sK2,sK3)
& h(sK2,X2) ) ) ) ),
introduced(choice_axiom,[]) ).
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_$i'(X0,X2)
| ( bomb(X0,X1)
& ~ defused(X0,X1)
& h(X0,X2) ) ) ) ),
inference(flattening,[],[f24]) ).
tff(f24,plain,
? [X0: '$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] :
( '$ki_exists_in_world_$i'(X0,X7)
& ( ( bomb(X0,X3)
& h(X0,X7) )
=> defused(X0,X3) ) ) ) ),
inference(negated_conjecture,[],[f8]) ).
tff(f8,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ? [X7] :
( '$ki_exists_in_world_$i'(X0,X7)
& ( ( bomb(X0,X3)
& h(X0,X7) )
=> defused(X0,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f65,plain,
~ '$ki_accessible'('$ki_local_world',sK2),
inference(resolution,[],[f63,f48]) ).
tff(f48,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f63,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK2) ),
inference(subsumption_resolution,[],[f61,f54]) ).
tff(f54,plain,
~ defused(sK2,sK3),
inference(subsumption_resolution,[],[f44,f53]) ).
tff(f53,plain,
! [X0: $i,X1: '$ki_world'] : '$ki_exists_in_world_$i'(X1,X0),
inference(cnf_transformation,[],[f38]) ).
tff(f38,plain,
! [X0,X1: '$ki_world'] : '$ki_exists_in_world_$i'(X1,X0),
inference(rectify,[],[f11]) ).
tff(f11,plain,
! [X1,X0: '$ki_world'] : '$ki_exists_in_world_$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(f44,plain,
! [X2: $i] :
( ~ defused(sK2,sK3)
| ~ '$ki_exists_in_world_$i'(sK2,X2) ),
inference(cnf_transformation,[],[f32]) ).
tff(f61,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK2)
| defused(sK2,sK3) ),
inference(resolution,[],[f59,f55]) ).
tff(f55,plain,
bomb(sK2,sK3),
inference(subsumption_resolution,[],[f45,f53]) ).
tff(f45,plain,
! [X2: $i] :
( bomb(sK2,sK3)
| ~ '$ki_exists_in_world_$i'(sK2,X2) ),
inference(cnf_transformation,[],[f32]) ).
tff(f59,plain,
! [X0: '$ki_world',X1: $i] :
( ~ bomb(sK2,X1)
| ~ '$ki_accessible'(X0,sK2)
| defused(sK2,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f58,f53]) ).
tff(f58,plain,
! [X0: '$ki_world',X1: $i] :
( ~ bomb(sK2,X1)
| defused(sK2,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK2) ),
inference(resolution,[],[f56,f39]) ).
tff(f39,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ h(X3,sK0(X0,X1))
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'(X0,X3)
| defused(X3,X1)
| ~ bomb(X3,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f27]) ).
tff(f27,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ( '$ki_exists_in_world_$i'(X0,sK0(X0,X1))
& ! [X3: '$ki_world'] :
( ~ '$ki_accessible'(X0,X3)
| defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,sK0(X0,X1)) ) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f26]) ).
tff(f26,plain,
! [X0: '$ki_world',X1] :
( ? [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
& ! [X3: '$ki_world'] :
( ~ '$ki_accessible'(X0,X3)
| defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,X2) ) )
=> ( '$ki_exists_in_world_$i'(X0,sK0(X0,X1))
& ! [X3: '$ki_world'] :
( ~ '$ki_accessible'(X0,X3)
| defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,sK0(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f21,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ? [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
& ! [X3: '$ki_world'] :
( ~ '$ki_accessible'(X0,X3)
| defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,X2) ) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f20]) ).
tff(f20,plain,
! [X0: '$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,[],[f14]) ).
tff(f14,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_$i'(X0,X2) ) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ? [X7] :
( '$ki_exists_in_world_$i'(X0,X7)
& ! [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
=> ( ( bomb(X6,X3)
& h(X6,X7) )
=> defused(X6,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f56,plain,
! [X2: $i] : h(sK2,X2),
inference(subsumption_resolution,[],[f43,f53]) ).
tff(f43,plain,
! [X2: $i] :
( h(sK2,X2)
| ~ '$ki_exists_in_world_$i'(sK2,X2) ),
inference(cnf_transformation,[],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : PLA053_4 : TPTP v8.2.0. Released v8.2.0.
% 0.10/0.12 % 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 : n008.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 12:28:53 EDT 2023
% 0.12/0.33 % CPUTime :
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% 0.97/0.62 % (3780)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/16Mi)
% 1.13/0.63 % (3794)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/99Mi)
% 1.13/0.63 % (3780)First to succeed.
% 1.18/0.64 % (3786)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/2Mi)
% 1.18/0.64 % (3780)Refutation found. Thanks to Tanya!
% 1.18/0.64 % SZS status Theorem for theBenchmark
% 1.18/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 1.18/0.64 % (3780)------------------------------
% 1.18/0.64 % (3780)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.18/0.64 % (3780)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.18/0.64 % (3780)Termination reason: Refutation
% 1.18/0.64
% 1.18/0.64 % (3780)Memory used [KB]: 1407
% 1.18/0.64 % (3780)Time elapsed: 0.103 s
% 1.18/0.64 % (3780)Instructions burned: 2 (million)
% 1.18/0.64 % (3780)------------------------------
% 1.18/0.64 % (3780)------------------------------
% 1.18/0.64 % (3632)Success in time 0.298 s
%------------------------------------------------------------------------------