%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PLA053_4 : 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 : n001.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 12:30:11 PM UTC 2026
% Result : Theorem 0.08s 0.46s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 18 unt; 0 typ; 6 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 176 ( 74 ~; 65 |; 21 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 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 : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 45 !; 9 ?; 54 :)
% 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'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f3,axiom,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f7,axiom,
! [X0: '$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'] :
( '$ki_accessible'(X0,X3)
=> ( ( bomb(X3,X1)
& h(X3,X2) )
=> defused(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f8,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2: $i] :
( '$ki_exists_in_world_$i'(X0,X2)
& ( ( bomb(X0,X1)
& h(X0,X2) )
=> defused(X0,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f9,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2: $i] :
( '$ki_exists_in_world_$i'(X0,X2)
& ( ( bomb(X0,X1)
& h(X0,X2) )
=> defused(X0,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
tff(f15,plain,
! [X0: '$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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f7]) ).
tff(f16,plain,
! [X0: '$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'('$ki_local_world',X0) ),
inference(flattening,[],[f15]) ).
tff(f17,plain,
? [X0: '$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'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f18,plain,
? [X0: '$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'('$ki_local_world',X0) ),
inference(flattening,[],[f17]) ).
tff(f22,plain,
! [X0: '$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))],[f16]) ).
tff(f23,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'('$ki_local_world',sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f18]) ).
tff(f24,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f26,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f3]) ).
tff(f32,plain,
! [X3: '$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,[],[f22]) ).
tff(f34,plain,
'$ki_accessible'('$ki_local_world',sK4),
inference(cnf_transformation,[],[f23]) ).
tff(f35,plain,
'$ki_exists_in_world_$i'(sK4,sK5),
inference(cnf_transformation,[],[f23]) ).
tff(f36,plain,
! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK4,X2)
| h(sK4,X2) ),
inference(cnf_transformation,[],[f23]) ).
tff(f37,plain,
! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK4,X2)
| bomb(sK4,sK5) ),
inference(cnf_transformation,[],[f23]) ).
tff(f38,plain,
! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK4,X2)
| ~ defused(sK4,sK5) ),
inference(cnf_transformation,[],[f23]) ).
tff(f40,definition,
( spl6_1
<=> defused(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
tff(f42,plain,
( ~ defused(sK4,sK5)
| spl6_1 ),
inference(avatar_component_clause,[],[f40]) ).
tff(f44,definition,
( spl6_2
<=> ! [X2: $i] : ~ '$ki_exists_in_world_$i'(sK4,X2) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
tff(f45,plain,
( ! [X2: $i] : ~ '$ki_exists_in_world_$i'(sK4,X2)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f44]) ).
tff(f46,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f38,f44,f40]) ).
tff(f48,definition,
( spl6_3
<=> ! [X2: $i] : h(sK4,X2) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
tff(f49,plain,
( ! [X2: $i] : h(sK4,X2)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f48]) ).
tff(f51,plain,
( $false
| ~ spl6_2 ),
inference(resolution,[],[f45,f35]) ).
tff(f52,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f51]) ).
tff(f54,definition,
( spl6_4
<=> bomb(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
tff(f56,plain,
( bomb(sK4,sK5)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f54]) ).
tff(f57,plain,
( spl6_4
| spl6_2 ),
inference(avatar_split_clause,[],[f37,f44,f54]) ).
tff(f58,plain,
! [X0: $i] : h(sK4,X0),
inference(resolution,[],[f26,f36]) ).
tff(f134,plain,
spl6_3,
inference(avatar_split_clause,[],[f58,f48]) ).
tff(f169,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ h(X3,sK3(X0,X1))
| ~ bomb(X3,X1)
| defused(X3,X1)
| ~ '$ki_accessible'(X0,X3)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f32,f26]) ).
tff(f206,plain,
( ! [X0: $i,X1: '$ki_world'] :
( ~ bomb(sK4,X0)
| defused(sK4,X0)
| ~ '$ki_accessible'(X1,sK4)
| ~ '$ki_accessible'('$ki_local_world',X1) )
| ~ spl6_3 ),
inference(resolution,[],[f169,f49]) ).
tff(f209,definition,
( spl6_21
<=> ! [X0: $i] :
( ~ bomb(sK4,X0)
| defused(sK4,X0) ) ),
introduced(definition,[new_symbols(definition,[spl6_21])],[avatar_definition]) ).
tff(f210,plain,
( ! [X0: $i] :
( ~ bomb(sK4,X0)
| defused(sK4,X0) )
| ~ spl6_21 ),
inference(avatar_component_clause,[],[f209]) ).
tff(f212,plain,
( defused(sK4,sK5)
| ~ spl6_4
| ~ spl6_21 ),
inference(resolution,[],[f210,f56]) ).
tff(f220,plain,
( $false
| spl6_1
| ~ spl6_4
| ~ spl6_21 ),
inference(forward_subsumption_resolution,[],[f212,f42]) ).
tff(f221,plain,
( spl6_1
| ~ spl6_4
| ~ spl6_21 ),
inference(avatar_contradiction_clause,[],[f220]) ).
tff(f226,definition,
( spl6_23
<=> ! [X1: '$ki_world'] :
( ~ '$ki_accessible'(X1,sK4)
| ~ '$ki_accessible'('$ki_local_world',X1) ) ),
introduced(definition,[new_symbols(definition,[spl6_23])],[avatar_definition]) ).
tff(f227,plain,
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,sK4) )
| ~ spl6_23 ),
inference(avatar_component_clause,[],[f226]) ).
tff(f228,plain,
( spl6_23
| spl6_21
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f206,f48,f209,f226]) ).
tff(f233,plain,
( ~ '$ki_accessible'(sK4,sK4)
| ~ spl6_23 ),
inference(resolution,[],[f227,f34]) ).
tff(f237,plain,
( $false
| ~ spl6_23 ),
inference(forward_subsumption_resolution,[],[f233,f24]) ).
tff(f238,plain,
~ spl6_23,
inference(avatar_contradiction_clause,[],[f237]) ).
cnf(s17,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f46]) ).
cnf(s27,plain,
~ spl6_2,
inference(sat_conversion,[],[f52]) ).
cnf(s30,plain,
( spl6_2
| spl6_4 ),
inference(sat_conversion,[],[f57]) ).
cnf(s83,plain,
spl6_3,
inference(sat_conversion,[],[f134]) ).
cnf(s145,plain,
( spl6_1
| ~ spl6_4
| ~ spl6_21 ),
inference(sat_conversion,[],[f221]) ).
cnf(s149,plain,
( ~ spl6_3
| spl6_21
| spl6_23 ),
inference(sat_conversion,[],[f228]) ).
cnf(s157,plain,
~ spl6_23,
inference(sat_conversion,[],[f238]) ).
cnf(s158,plain,
( ~ spl6_3
| spl6_21 ),
inference(rat,[],[s149,s157]) ).
cnf(s159,plain,
spl6_21,
inference(rat,[],[s158,s83]) ).
cnf(s162,plain,
spl6_4,
inference(rat,[],[s30,s27]) ).
cnf(s163,plain,
spl6_1,
inference(rat,[],[s145,s159,s162]) ).
cnf(s165,plain,
$false,
inference(rat,[],[s17,s27,s163]) ).
tff(f239,plain,
$false,
inference(avatar_sat_refutation,[],[s165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PLA053_4 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.37 % Computer : n001.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 22:20:33 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.42 Running first-order model finding
% 0.08/0.42 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
% 0.08/0.46 % (4018605)Will run a generic schedule for satisfiability detection.
% 0.08/0.46 % (4018612)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3580023961:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.46 % (4018612) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4018605-4018612"...
% 0.08/0.46 % (4018612)...printing done.
% 0.08/0.46 % (4018611)% WARNING: option uhcvi not known.
% 0.08/0.46 % (4018612)Refutation found. Thanks to Tanya!
% 0.08/0.46 % SZS status Theorem for theBenchmark
% 0.08/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.46 % (4018612)------------------------------
% 0.08/0.46 % (4018612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.46 % (4018612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.46 % (4018612)CaDiCaL version: 2.1.3
% 0.08/0.46 % (4018612)Termination reason: Refutation
% 0.08/0.46 % (4018612)Time elapsed: 0.004 s
% 0.08/0.46 % (4018612)Peak memory usage: 12 MB
% 0.08/0.46 % (4018612)Instructions burned: 5 (million)
% 0.08/0.46 % (4018605)Success in time 0.025 s
% 0.08/0.46 % Vampire exiting
%------------------------------------------------------------------------------