%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PLA053_5 : 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 : n015.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 2.81s 1.36s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 115 ( 46 ~; 38 |; 21 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 55 ( 46 !; 9 ?; 55 :)
% 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 ) > $o ).
tff(f1,axiom,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
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_$i'(X0,X2)
& ( ( bomb(X0,X1)
& h(X0,X2) )
=> defused(X0,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
tff(f9,plain,
? [X0: '$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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f8]) ).
tff(f10,plain,
? [X0: '$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'('$ki_local_world',X0) ),
inference(flattening,[],[f9]) ).
tff(f14,plain,
! [X0: '$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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f6]) ).
tff(f15,plain,
! [X0: '$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,[],[f14]) ).
tff(f16,plain,
( ! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X2)
| ( ~ defused(sK0,sK1)
& bomb(sK0,sK1)
& h(sK0,X2) ) )
& '$ki_exists_in_world_$i'(sK0,sK1)
& '$ki_accessible'('$ki_local_world',sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
tff(f19,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ( '$ki_exists_in_world_$i'(X0,sK4(X0,X1))
& ! [X3: '$ki_world'] :
( defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,sK4(X0,X1))
| ~ '$ki_accessible'(X0,X3) ) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f15]) ).
tff(f22,plain,
'$ki_exists_in_world_$i'(sK0,sK1),
inference(cnf_transformation,[],[f16]) ).
tff(f23,plain,
! [X2: $i] :
( h(sK0,X2)
| ~ '$ki_exists_in_world_$i'(sK0,X2) ),
inference(cnf_transformation,[],[f16]) ).
tff(f24,plain,
! [X2: $i] :
( bomb(sK0,sK1)
| ~ '$ki_exists_in_world_$i'(sK0,X2) ),
inference(cnf_transformation,[],[f16]) ).
tff(f25,plain,
! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X2)
| ~ defused(sK0,sK1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f28,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f1]) ).
tff(f31,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,sK4(X0,X1))
| ~ '$ki_accessible'(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f19]) ).
tff(f34,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f2]) ).
tff(f35,plain,
~ defused(sK0,sK1),
inference(resolution,[],[f25,f22]) ).
tff(f41,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,sK4(X0,X1))
| ~ '$ki_accessible'(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X1) ),
inference(forward_subsumption_resolution,[],[f31,f28]) ).
tff(f42,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,sK4(X0,X1))
| ~ '$ki_exists_in_world_$i'(X0,X1) ),
inference(forward_subsumption_resolution,[],[f41,f28]) ).
tff(f43,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ h(X3,sK4(X0,X1))
| ~ bomb(X3,X1)
| defused(X3,X1) ),
inference(forward_subsumption_resolution,[],[f42,f34]) ).
tff(f44,plain,
! [X0: $i,X1: '$ki_world'] :
( ~ bomb(sK0,X0)
| defused(sK0,X0)
| ~ '$ki_exists_in_world_$i'(sK0,sK4(X1,X0)) ),
inference(resolution,[],[f43,f23]) ).
tff(f45,plain,
! [X0: $i] :
( defused(sK0,X0)
| ~ bomb(sK0,X0) ),
inference(forward_subsumption_resolution,[],[f44,f34]) ).
tff(f46,plain,
~ bomb(sK0,sK1),
inference(resolution,[],[f45,f35]) ).
tff(f47,plain,
! [X0: $i] : ~ '$ki_exists_in_world_$i'(sK0,X0),
inference(resolution,[],[f46,f24]) ).
tff(f49,plain,
$false,
inference(forward_subsumption_resolution,[],[f47,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA053_5 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:18:46 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.81/1.36 % (2072012)Detected formulas, will run a generic FOF schedule.
% 2.81/1.36 % (2072021)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2624444417:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.81/1.36 % (2072021)First to succeed.
% 2.81/1.36 % (2072021)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2072012"
% 2.81/1.36 % (2072018)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=1986051624:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.81/1.36 % (2072023)dis-21_1_sil=8000:lcm=predicate:random_seed=1311066506: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)
% 2.81/1.36 % (2072019)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=351521526:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.81/1.36 % (2072017)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=2303720059:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.81/1.36 % (2072020)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1465877579:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.81/1.36 % (2072020)Also succeeded, but the first one will report.
% 2.81/1.36 % (2072023)Also succeeded, but the first one will report.
% 2.81/1.36 % (2072022)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=573430491:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.81/1.36 % (2072022)Also succeeded, but the first one will report.
% 2.81/1.36 % (2072021)Refutation found. Thanks to Tanya!
% 2.81/1.36 % SZS status Theorem for theBenchmark
% 2.81/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.81/1.36 % (2072021)------------------------------
% 2.81/1.36 % (2072021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.36 % (2072021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.36 % (2072021)CaDiCaL version: 2.1.3
% 2.81/1.36 % (2072021)Termination reason: Refutation
% 2.81/1.36 % (2072021)Time elapsed: 0.001 s
% 2.81/1.36 % (2072021)Peak memory usage: 88 MB
% 2.81/1.36 % (2072021)Instructions burned: 1 (million)
% 2.81/1.36 % (2072021)------------------------------
% 2.81/1.36 % (2072021)------------------------------
% 2.81/1.36 % (2072012)Success in time 0.314 s
% 2.81/1.36 % Vampire exiting
%------------------------------------------------------------------------------