%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PLA053_2 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:28:31 PM UTC 2026
% Result : Theorem 2.52s 1.33s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 19 unt; 0 typ; 7 def)
% Number of atoms : 192 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 188 ( 81 ~; 69 |; 21 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 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 : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 13 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 37 !; 9 ?; 46 :)
% 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 ) > $o ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f2,axiom,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f6,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2: $i] :
( '$ki_exists_in_world_$i'(X0,X2)
& ! [X3: '$ki_world'] :
( '$ki_accessible'(X0,X3)
=> ( ( bomb(X3,X1)
& h(X3,X2) )
=> defused(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f7,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2: $i] :
( '$ki_exists_in_world_$i'(X0,X2)
& ( ( bomb(X0,X1)
& h(X0,X2) )
=> defused(X0,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f8,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2: $i] :
( '$ki_exists_in_world_$i'(X0,X2)
& ( ( bomb(X0,X1)
& h(X0,X2) )
=> defused(X0,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
tff(f12,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ? [X2: $i] :
( '$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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f6]) ).
tff(f13,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ? [X2: $i] :
( '$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'('$ki_local_world',X0) ),
inference(flattening,[],[f12]) ).
tff(f14,plain,
? [X0: '$ki_world'] :
( ? [X1: $i] :
( ! [X2: $i] :
( ~ '$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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f8]) ).
tff(f15,plain,
? [X0: '$ki_world'] :
( ? [X1: $i] :
( ! [X2: $i] :
( ~ '$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'('$ki_local_world',X0) ),
inference(flattening,[],[f14]) ).
tff(f19,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ( '$ki_exists_in_world_$i'(X0,sK3(X0,X1))
& ! [X3: '$ki_world'] :
( defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,sK3(X0,X1))
| ~ '$ki_accessible'(X0,X3) ) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f13]) ).
tff(f20,plain,
( ! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK4,X2)
| ( ~ defused(sK4,sK5)
& bomb(sK4,sK5)
& h(sK4,X2) ) )
& '$ki_exists_in_world_$i'(sK4,sK5)
& '$ki_accessible'('$ki_local_world',sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f15]) ).
tff(f21,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f22,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f2]) ).
tff(f28,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,sK3(X0,X1))
| ~ '$ki_accessible'(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f19]) ).
tff(f30,plain,
'$ki_accessible'('$ki_local_world',sK4),
inference(cnf_transformation,[],[f20]) ).
tff(f31,plain,
'$ki_exists_in_world_$i'(sK4,sK5),
inference(cnf_transformation,[],[f20]) ).
tff(f32,plain,
! [X2: $i] :
( h(sK4,X2)
| ~ '$ki_exists_in_world_$i'(sK4,X2) ),
inference(cnf_transformation,[],[f20]) ).
tff(f33,plain,
! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK4,X2)
| bomb(sK4,sK5) ),
inference(cnf_transformation,[],[f20]) ).
tff(f34,plain,
! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK4,X2)
| ~ defused(sK4,sK5) ),
inference(cnf_transformation,[],[f20]) ).
tff(f36,definition,
( spl6_1
<=> bomb(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
tff(f39,definition,
( spl6_2
<=> ! [X2: $i] : ~ '$ki_exists_in_world_$i'(sK4,X2) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
tff(f40,plain,
( ! [X2: $i] : ~ '$ki_exists_in_world_$i'(sK4,X2)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f41,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f33,f39,f36]) ).
tff(f43,definition,
( spl6_3
<=> defused(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
tff(f44,plain,
( ~ defused(sK4,sK5)
| spl6_3 ),
inference(avatar_component_clause,[],[f43]) ).
tff(f45,plain,
( ~ spl6_3
| spl6_2 ),
inference(avatar_split_clause,[],[f34,f39,f43]) ).
tff(f46,plain,
( $false
| ~ spl6_2 ),
inference(resolution,[],[f31,f40]) ).
tff(f47,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f46]) ).
tff(f53,definition,
( spl6_5
<=> '$ki_accessible'('$ki_local_world',sK4) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
tff(f54,plain,
( ~ '$ki_accessible'('$ki_local_world',sK4)
| spl6_5 ),
inference(avatar_component_clause,[],[f53]) ).
tff(f61,plain,
( $false
| spl6_5 ),
inference(resolution,[],[f54,f30]) ).
tff(f62,plain,
spl6_5,
inference(avatar_contradiction_clause,[],[f61]) ).
tff(f63,plain,
( ! [X0: '$ki_world'] :
( ~ bomb(sK4,sK5)
| ~ h(sK4,sK3(X0,sK5))
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_exists_in_world_$i'(X0,sK5)
| ~ '$ki_accessible'('$ki_local_world',X0) )
| spl6_3 ),
inference(resolution,[],[f28,f44]) ).
tff(f65,definition,
( spl6_7
<=> ! [X0: '$ki_world'] :
( ~ h(sK4,sK3(X0,sK5))
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'(X0,sK5)
| ~ '$ki_accessible'(X0,sK4) ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
tff(f66,plain,
( ! [X0: '$ki_world'] :
( ~ h(sK4,sK3(X0,sK5))
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'(X0,sK5)
| ~ '$ki_accessible'(X0,sK4) )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f65]) ).
tff(f68,plain,
( spl6_7
| ~ spl6_1
| spl6_3 ),
inference(avatar_split_clause,[],[f63,f43,f36,f65]) ).
tff(f69,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_exists_in_world_$i'(X0,sK5)
| ~ '$ki_exists_in_world_$i'(sK4,sK3(X0,sK5)) )
| ~ spl6_7 ),
inference(resolution,[],[f66,f32]) ).
tff(f71,plain,
( ~ '$ki_accessible'('$ki_local_world',sK4)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',sK5)
| ~ '$ki_exists_in_world_$i'(sK4,sK3('$ki_local_world',sK5))
| ~ spl6_7 ),
inference(resolution,[],[f69,f21]) ).
tff(f73,definition,
( spl6_8
<=> '$ki_exists_in_world_$i'(sK4,sK3('$ki_local_world',sK5)) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
tff(f74,plain,
( ~ '$ki_exists_in_world_$i'(sK4,sK3('$ki_local_world',sK5))
| spl6_8 ),
inference(avatar_component_clause,[],[f73]) ).
tff(f76,definition,
( spl6_9
<=> '$ki_exists_in_world_$i'('$ki_local_world',sK5) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
tff(f77,plain,
( ~ '$ki_exists_in_world_$i'('$ki_local_world',sK5)
| spl6_9 ),
inference(avatar_component_clause,[],[f76]) ).
tff(f78,plain,
( ~ spl6_8
| ~ spl6_9
| ~ spl6_5
| ~ spl6_7 ),
inference(avatar_split_clause,[],[f71,f65,f53,f76,f73]) ).
tff(f91,plain,
( $false
| spl6_8 ),
inference(resolution,[],[f74,f22]) ).
tff(f92,plain,
spl6_8,
inference(avatar_contradiction_clause,[],[f91]) ).
tff(f93,plain,
( $false
| spl6_9 ),
inference(resolution,[],[f77,f22]) ).
tff(f94,plain,
spl6_9,
inference(avatar_contradiction_clause,[],[f93]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f41]) ).
cnf(s2,plain,
( spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f45]) ).
cnf(s3,plain,
~ spl6_2,
inference(sat_conversion,[],[f47]) ).
cnf(s6,plain,
spl6_5,
inference(sat_conversion,[],[f62]) ).
cnf(s7,plain,
( ~ spl6_1
| spl6_3
| spl6_7 ),
inference(sat_conversion,[],[f68]) ).
cnf(s8,plain,
( ~ spl6_5
| ~ spl6_7
| ~ spl6_8
| ~ spl6_9 ),
inference(sat_conversion,[],[f78]) ).
cnf(s11,plain,
spl6_8,
inference(sat_conversion,[],[f92]) ).
cnf(s12,plain,
spl6_9,
inference(sat_conversion,[],[f94]) ).
cnf(s14,plain,
( ~ spl6_5
| ~ spl6_7 ),
inference(rat,[],[s8,s12,s11]) ).
cnf(s15,plain,
~ spl6_7,
inference(rat,[],[s14,s6]) ).
cnf(s17,plain,
~ spl6_3,
inference(rat,[],[s2,s3]) ).
cnf(s18,plain,
~ spl6_1,
inference(rat,[],[s7,s15,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s3,s18]) ).
tff(f95,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PLA053_2 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n014.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 22:14:47 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.52/1.33 % (1222038)Detected formulas, will run a generic FOF schedule.
% 2.52/1.33 % (1222049)dis-21_1_sil=8000:lcm=predicate:random_seed=3228067533:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.52/1.33 % (1222049)First to succeed.
% 2.52/1.33 % (1222049)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1222038"
% 2.52/1.33 % (1222047)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1686305696:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.52/1.33 % (1222044)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1698302144:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.52/1.33 % (1222045)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1405016905:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.52/1.33 % (1222046)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2468491303:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.52/1.33 % (1222043)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2107756132:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.52/1.33 % (1222048)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3870749360:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.52/1.33 % (1222047)Also succeeded, but the first one will report.
% 2.52/1.33 % (1222046)Also succeeded, but the first one will report.
% 2.52/1.33 % (1222048)Also succeeded, but the first one will report.
% 2.52/1.33 % (1222049)Refutation found. Thanks to Tanya!
% 2.52/1.33 % SZS status Theorem for theBenchmark
% 2.52/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.52/1.33 % (1222049)------------------------------
% 2.52/1.33 % (1222049)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.33 % (1222049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.33 % (1222049)CaDiCaL version: 2.1.3
% 2.52/1.33 % (1222049)Termination reason: Refutation
% 2.52/1.33 % (1222049)Time elapsed: 0.002 s
% 2.52/1.33 % (1222049)Peak memory usage: 89 MB
% 2.52/1.33 % (1222049)Instructions burned: 2 (million)
% 2.52/1.33 % (1222049)------------------------------
% 2.52/1.33 % (1222049)------------------------------
% 2.52/1.33 % (1222038)Success in time 0.275 s
% 2.52/1.33 % Vampire exiting
%------------------------------------------------------------------------------