%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO886_6 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 02:29:15 PM UTC 2026
% Result : Theorem 0.21s 1.13s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 63 ( 22 ~; 15 |; 9 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 28 ( 0 sgn 24 !; 4 ?; 28 :)
% 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' > '$ki_world' ).
tff(func_def_2,type,
sK1: '$ki_world' > $i ).
tff(func_def_3,type,
sK2: '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
f: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f2,axiom,
! [X0: '$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(f4,conjecture,
( ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> f(X1,X0) ) )
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ! [X0: $i] :
( '$ki_exists_in_world_$i'(X1,X0)
=> f(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f5,negated_conjecture,
~ ( ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> f(X1,X0) ) )
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ! [X0: $i] :
( '$ki_exists_in_world_$i'(X1,X0)
=> f(X1,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f6,plain,
~ ( ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> f(X1,X0) ) )
=> ! [X2: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X2)
=> ! [X3: $i] :
( '$ki_exists_in_world_$i'(X2,X3)
=> f(X2,X3) ) ) ),
inference(rectify,[],[f5]) ).
tff(f7,plain,
( ? [X2: '$ki_world'] :
( ? [X3: $i] :
( ~ f(X2,X3)
& '$ki_exists_in_world_$i'(X2,X3) )
& '$ki_accessible'('$ki_local_world',X2) )
& ! [X0: $i] :
( ! [X1: '$ki_world'] :
( f(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ) ),
inference(ennf_transformation,[],[f6]) ).
tff(f10,plain,
( ? [X0: '$ki_world'] :
( ? [X1: $i] :
( ~ f(X0,X1)
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) )
& ! [X2: $i] :
( ! [X3: '$ki_world'] :
( f(X3,X2)
| ~ '$ki_accessible'('$ki_local_world',X3) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X2) ) ),
inference(rectify,[],[f7]) ).
tff(f11,plain,
( ~ f(sK2,sK3)
& '$ki_exists_in_world_$i'(sK2,sK3)
& '$ki_accessible'('$ki_local_world',sK2)
& ! [X2: $i] :
( ! [X3: '$ki_world'] :
( f(X3,X2)
| ~ '$ki_accessible'('$ki_local_world',X3) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f10]) ).
tff(f13,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f2]) ).
tff(f15,plain,
! [X2: $i,X3: '$ki_world'] :
( f(X3,X2)
| ~ '$ki_accessible'('$ki_local_world',X3)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X2) ),
inference(cnf_transformation,[],[f11]) ).
tff(f16,plain,
'$ki_accessible'('$ki_local_world',sK2),
inference(cnf_transformation,[],[f11]) ).
tff(f18,plain,
~ f(sK2,sK3),
inference(cnf_transformation,[],[f11]) ).
tff(f19,plain,
( ~ '$ki_accessible'('$ki_local_world',sK2)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',sK3) ),
inference(resolution,[],[f15,f18]) ).
tff(f21,definition,
( spl4_1
<=> '$ki_exists_in_world_$i'('$ki_local_world',sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f22,plain,
( ~ '$ki_exists_in_world_$i'('$ki_local_world',sK3)
| spl4_1 ),
inference(avatar_component_clause,[],[f21]) ).
tff(f24,definition,
( spl4_2
<=> '$ki_accessible'('$ki_local_world',sK2) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f25,plain,
( ~ '$ki_accessible'('$ki_local_world',sK2)
| spl4_2 ),
inference(avatar_component_clause,[],[f24]) ).
tff(f26,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f19,f24,f21]) ).
tff(f27,plain,
( $false
| spl4_1 ),
inference(resolution,[],[f13,f22]) ).
tff(f28,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f27]) ).
tff(f29,plain,
( $false
| spl4_2 ),
inference(resolution,[],[f25,f16]) ).
tff(f30,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f29]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s2,plain,
spl4_1,
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
spl4_2,
inference(sat_conversion,[],[f30]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
tff(f31,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO886_6 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n026.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 18:42:27 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/1.13 % (4129509)Detected formulas, will run a generic FOF schedule.
% 0.21/1.13 % (4129567)dis-21_1_sil=8000:lcm=predicate:random_seed=4150128597: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)
% 0.21/1.13 % (4129567)First to succeed.
% 0.21/1.13 % (4129567)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4129509"
% 0.21/1.13 % (4129566)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2793196427:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.21/1.13 % (4129565)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4027430723:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.21/1.13 % (4129562)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=521391351:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.21/1.13 % (4129561)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=407508062:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.21/1.13 % (4129563)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=3723612011:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.21/1.13 % (4129565)Also succeeded, but the first one will report.
% 0.21/1.13 % (4129566)Also succeeded, but the first one will report.
% 0.21/1.13 % (4129564)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3761262639:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.21/1.13 % (4129564)Also succeeded, but the first one will report.
% 0.21/1.13 % (4129567)Refutation found. Thanks to Tanya!
% 0.21/1.13 % SZS status Theorem for theBenchmark
% 0.21/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.13 % (4129567)------------------------------
% 0.21/1.13 % (4129567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.13 % (4129567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.13 % (4129567)CaDiCaL version: 2.1.3
% 0.21/1.13 % (4129567)Termination reason: Refutation
% 0.21/1.13 % (4129567)Time elapsed: 0.001 s
% 0.21/1.13 % (4129567)Peak memory usage: 89 MB
% 0.21/1.13 % (4129567)Instructions burned: 1 (million)
% 0.21/1.13 % (4129567)------------------------------
% 0.21/1.13 % (4129567)------------------------------
% 0.21/1.13 % (4129509)Success in time 0.266 s
% 0.21/1.13 % Vampire exiting
%------------------------------------------------------------------------------