%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL962_16 : 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 : n013.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 12:01:18 PM UTC 2026
% Result : Theorem 0.23s 0.54s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 14 unt; 0 typ; 3 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 123 ( 52 ~; 53 |; 2 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 41 ( 0 sgn 39 !; 2 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(type_def_6,type,
'$ki_index': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_1,type,
'#idx(a)': '$ki_index' ).
tff(func_def_2,type,
'#idx(b)': '$ki_index' ).
tff(func_def_3,type,
sK0: '$ki_world' > '$ki_world' ).
tff(func_def_4,type,
sK1: '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_index' * '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
p: '$ki_world' > $o ).
tff(f3,axiom,
! [X0: '$ki_world'] : '$ki_accessible'('#idx(b)',X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_reflexive_#idx(b)') ).
tff(f5,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
=> ( p(X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X0,X1)
=> p(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_1) ).
tff(f6,axiom,
( ~ ! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(b)','$ki_local_world',X0)
=> p(X0) )
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
=> ~ ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X0,X1)
=> p(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_2) ).
tff(f7,axiom,
~ p('$ki_local_world'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_a_axiom_1) ).
tff(f8,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
=> ~ p(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f9,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
=> ~ p(X0) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
tff(f10,plain,
( ~ ! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(b)','$ki_local_world',X0)
=> p(X0) )
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X1)
=> ~ ! [X2: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X1,X2)
=> p(X2) ) ) ),
inference(rectify,[],[f6]) ).
tff(f15,plain,
! [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( p(X1)
| ~ '$ki_accessible'('#idx(b)',X0,X1) )
| ~ p(X0)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
inference(ennf_transformation,[],[f5]) ).
tff(f16,plain,
! [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( p(X1)
| ~ '$ki_accessible'('#idx(b)',X0,X1) )
| ~ p(X0)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
inference(flattening,[],[f15]) ).
tff(f17,plain,
( ! [X1: '$ki_world'] :
( ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'('#idx(b)',X1,X2) )
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1) )
| ! [X0: '$ki_world'] :
( p(X0)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0) ) ),
inference(ennf_transformation,[],[f10]) ).
tff(f18,plain,
? [X0: '$ki_world'] :
( p(X0)
& '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f21,plain,
! [X0: '$ki_world'] : '$ki_accessible'('#idx(b)',X0,X0),
inference(cnf_transformation,[],[f3]) ).
tff(f23,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
| ~ p(X0)
| ~ '$ki_accessible'('#idx(b)',X0,X1)
| p(X1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f24,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0)
| p(X0)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1)
| '$ki_accessible'('#idx(b)',X1,sK0(X1)) ),
inference(cnf_transformation,[],[f17]) ).
tff(f25,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0)
| p(X0)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1)
| ~ p(sK0(X1)) ),
inference(cnf_transformation,[],[f17]) ).
tff(f26,plain,
~ p('$ki_local_world'),
inference(cnf_transformation,[],[f7]) ).
tff(f27,plain,
'$ki_accessible'('#idx(a)','$ki_local_world',sK1),
inference(cnf_transformation,[],[f18]) ).
tff(f28,plain,
p(sK1),
inference(cnf_transformation,[],[f18]) ).
tff(f31,plain,
! [X0: '$ki_world'] : ~ '$ki_accessible'('#idx(b)',X0,X0),
inference(consistent_polarity_flipping,[],[f21]) ).
tff(f33,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ p(X0)
| '$ki_accessible'('#idx(a)','$ki_local_world',X0)
| '$ki_accessible'('#idx(b)',X0,X1)
| p(X1) ),
inference(consistent_polarity_flipping,[],[f23]) ).
tff(f34,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( '$ki_accessible'('#idx(b)','$ki_local_world',X0)
| p(X0)
| '$ki_accessible'('#idx(a)','$ki_local_world',X1)
| ~ p(sK0(X1)) ),
inference(consistent_polarity_flipping,[],[f25]) ).
tff(f35,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( '$ki_accessible'('#idx(b)','$ki_local_world',X0)
| p(X0)
| '$ki_accessible'('#idx(a)','$ki_local_world',X1)
| ~ '$ki_accessible'('#idx(b)',X1,sK0(X1)) ),
inference(consistent_polarity_flipping,[],[f24]) ).
tff(f36,plain,
~ '$ki_accessible'('#idx(a)','$ki_local_world',sK1),
inference(consistent_polarity_flipping,[],[f27]) ).
tff(f38,definition,
( spl2_1
<=> ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X1)
| ~ '$ki_accessible'('#idx(b)',X1,sK0(X1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f39,plain,
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)',X1,sK0(X1))
| '$ki_accessible'('#idx(a)','$ki_local_world',X1) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f38]) ).
tff(f41,definition,
( spl2_2
<=> ! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(b)','$ki_local_world',X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f42,plain,
( ! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(b)','$ki_local_world',X0)
| p(X0) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f41]) ).
tff(f43,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f35,f41,f38]) ).
tff(f45,definition,
( spl2_3
<=> ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X1)
| ~ p(sK0(X1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f46,plain,
( ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X1)
| ~ p(sK0(X1)) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f45]) ).
tff(f47,plain,
( spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f34,f41,f45]) ).
tff(f48,plain,
( p('$ki_local_world')
| ~ spl2_2 ),
inference(resolution,[],[f42,f31]) ).
tff(f49,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f48,f26]) ).
tff(f50,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f49]) ).
tff(f54,plain,
! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',sK1)
| '$ki_accessible'('#idx(b)',sK1,X0)
| p(X0) ),
inference(resolution,[],[f33,f28]) ).
tff(f55,plain,
! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(b)',sK1,X0)
| p(X0) ),
inference(forward_subsumption_resolution,[],[f54,f36]) ).
tff(f57,plain,
( p(sK0(sK1))
| '$ki_accessible'('#idx(a)','$ki_local_world',sK1)
| ~ spl2_1 ),
inference(resolution,[],[f55,f39]) ).
tff(f59,plain,
( '$ki_accessible'('#idx(a)','$ki_local_world',sK1)
| ~ spl2_1
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f57,f46]) ).
tff(f60,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f59,f36]) ).
tff(f61,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f60]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s2,plain,
( spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f50]) ).
cnf(s4,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f61]) ).
cnf(s5,plain,
spl2_3,
inference(rat,[],[s2,s3]) ).
cnf(s6,plain,
~ spl2_1,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s3,s6]) ).
tff(f62,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL962_16 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.19/0.44 % Computer : n013.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 17:08:06 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.23/0.50 Running first-order model finding
% 0.23/0.50 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
% 0.23/0.54 % (428917)Will run a generic schedule for satisfiability detection.
% 0.23/0.54 % (428923)% WARNING: option uhcvi not known.
% 0.23/0.54 % (428923)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3159443462:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.23/0.54 % (428923) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-428917-428923"...
% 0.23/0.54 % (428923)...printing done.
% 0.23/0.54 % (428923)Refutation found. Thanks to Tanya!
% 0.23/0.54 % SZS status Theorem for theBenchmark
% 0.23/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.54 % (428923)------------------------------
% 0.23/0.54 % (428923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.54 % (428923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.54 % (428923)CaDiCaL version: 2.1.3
% 0.23/0.54 % (428923)Termination reason: Refutation
% 0.23/0.54 % (428923)Time elapsed: 0.002 s
% 0.23/0.54 % (428923)Peak memory usage: 12 MB
% 0.23/0.54 % (428923)Instructions burned: 2 (million)
% 0.23/0.54 % (428917)Success in time 0.025 s
% 0.23/0.54 % Vampire exiting
%------------------------------------------------------------------------------