%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PLA053_2 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 12:30:10 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 11 unt; 0 typ; 3 def)
% Number of atoms : 139 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 146 ( 62 ~; 55 |; 16 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 13 ( 13 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 34 !; 9 ?; 43 :)
% 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'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f2,axiom,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$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'] :
( '$ki_accessible'(X0,X3)
=> ( ( bomb(X3,X1)
& h(X3,X2) )
=> defused(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f7,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2: $i] :
( '$ki_exists_in_world_$i'(X0,X2)
& ( ( bomb(X0,X1)
& h(X0,X2) )
=> defused(X0,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f8,negated_conjecture,
~ ! [X0: '$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'('$ki_local_world',X0) ),
inference(flattening,[],[f14]) ).
tff(f16,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f17,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f2]) ).
tff(f23,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( defused(X3,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'(X0,X3)
| ~ h(X3,sK3(X0,X1))
| ~ bomb(X3,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f13]) ).
tff(f25,plain,
! [X2: $i] :
( h(sK4,X2)
| ~ '$ki_exists_in_world_$i'(sK4,X2) ),
inference(cnf_transformation,[],[f15]) ).
tff(f26,plain,
! [X2: $i] :
( bomb(sK4,sK5)
| ~ '$ki_exists_in_world_$i'(sK4,X2) ),
inference(cnf_transformation,[],[f15]) ).
tff(f27,plain,
! [X2: $i] :
( ~ defused(sK4,sK5)
| ~ '$ki_exists_in_world_$i'(sK4,X2) ),
inference(cnf_transformation,[],[f15]) ).
tff(f29,plain,
'$ki_accessible'('$ki_local_world',sK4),
inference(cnf_transformation,[],[f15]) ).
tff(f31,definition,
( spl6_1
<=> ! [X2: $i] : ~ '$ki_exists_in_world_$i'(sK4,X2) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
tff(f32,plain,
( ! [X2: $i] : ~ '$ki_exists_in_world_$i'(sK4,X2)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f31]) ).
tff(f34,definition,
( spl6_2
<=> bomb(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
tff(f36,plain,
( bomb(sK4,sK5)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f34]) ).
tff(f37,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f26,f34,f31]) ).
tff(f39,definition,
( spl6_3
<=> defused(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
tff(f41,plain,
( ~ defused(sK4,sK5)
| spl6_3 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f42,plain,
( spl6_1
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f27,f39,f31]) ).
tff(f51,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK5)
| ~ '$ki_accessible'(X0,sK4)
| ~ h(sK4,sK3(X0,sK5))
| ~ bomb(sK4,sK5)
| ~ '$ki_accessible'('$ki_local_world',X0) )
| spl6_3 ),
inference(resolution,[],[f23,f41]) ).
tff(f52,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,sK5)
| ~ '$ki_accessible'(X0,sK4)
| ~ h(sK4,sK3(X0,sK5))
| ~ '$ki_accessible'('$ki_local_world',X0) )
| ~ spl6_2
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f51,f36]) ).
tff(f53,plain,
( ! [X0: '$ki_world'] :
( ~ h(sK4,sK3(X0,sK5))
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_accessible'('$ki_local_world',X0) )
| ~ spl6_2
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f52,f17]) ).
tff(f59,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'(sK4,sK3(X0,sK5)) )
| ~ spl6_2
| spl6_3 ),
inference(resolution,[],[f53,f25]) ).
tff(f60,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_accessible'('$ki_local_world',X0) )
| ~ spl6_2
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f59,f17]) ).
tff(f62,plain,
( ~ '$ki_accessible'(sK4,sK4)
| ~ spl6_2
| spl6_3 ),
inference(resolution,[],[f60,f29]) ).
tff(f66,plain,
( $false
| ~ spl6_2
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f62,f16]) ).
tff(f67,plain,
( ~ spl6_2
| spl6_3 ),
inference(avatar_contradiction_clause,[],[f66]) ).
tff(f68,plain,
( $false
| ~ spl6_1 ),
inference(forward_subsumption_resolution,[],[f32,f17]) ).
tff(f69,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f68]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f37]) ).
cnf(s2,plain,
( spl6_1
| ~ spl6_3 ),
inference(sat_conversion,[],[f42]) ).
cnf(s4,plain,
( ~ spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f67]) ).
cnf(s5,plain,
~ spl6_1,
inference(sat_conversion,[],[f69]) ).
cnf(s6,plain,
~ spl6_3,
inference(rat,[],[s2,s5]) ).
cnf(s7,plain,
~ spl6_2,
inference(rat,[],[s4,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s5]) ).
tff(f70,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA053_2 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n020.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 22:15:35 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.44 % (3814921)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (3814930)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3845957621:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.44 % (3814930) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3814921-3814930"...
% 0.11/0.44 % (3814930)...printing done.
% 0.11/0.44 % (3814927)% WARNING: option uhcvi not known.
% 0.11/0.44 % (3814930)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.44 % (3814930)------------------------------
% 0.11/0.44 % (3814930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.44 % (3814930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.44 % (3814930)CaDiCaL version: 2.1.3
% 0.11/0.44 % (3814930)Termination reason: Refutation
% 0.11/0.44 % (3814930)Time elapsed: 0.002 s
% 0.11/0.44 % (3814930)Peak memory usage: 12 MB
% 0.11/0.44 % (3814930)Instructions burned: 2 (million)
% 0.11/0.44 % (3814921)Success in time 0.026 s
% 0.11/0.44 % Vampire exiting
%------------------------------------------------------------------------------