%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO891_16 : 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 : 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 02:29:17 PM UTC 2026
% Result : Theorem 2.21s 0.88s
% Output : Refutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 125 ( 41 ~; 33 |; 36 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 8 ( 7 usr; 4 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 37 !; 24 ?; 61 :)
% 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' > $i ).
tff(func_def_3,type,
sK2: '$ki_world' ).
tff(func_def_4,type,
sK3: ( $i * '$ki_world' ) > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
qmltpeq: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_3,type,
p: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f3,axiom,
! [X0: '$ki_world',X1: '$ki_world',X2: $i] :
( ( '$ki_exists_in_world_$i'(X0,X2)
& '$ki_accessible'(X0,X1) )
=> '$ki_exists_in_world_$i'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_cumul') ).
tff(f9,conjecture,
( ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ? [X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
& qmltpeq(X1,X0,X2) ) ) )
=> ( ? [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ? [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
& p(X1,X0) ) )
=> ? [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
& ? [X0: $i] :
( '$ki_exists_in_world_$i'(X1,X0)
& p(X1,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f10,negated_conjecture,
~ ( ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ? [X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
& qmltpeq(X1,X0,X2) ) ) )
=> ( ? [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ? [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
& p(X1,X0) ) )
=> ? [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
& ? [X0: $i] :
( '$ki_exists_in_world_$i'(X1,X0)
& p(X1,X0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
tff(f11,plain,
~ ( ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ? [X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
& qmltpeq(X1,X0,X2) ) ) )
=> ( ? [X3: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
& ? [X4: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X4)
& p(X4,X3) ) )
=> ? [X5: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X5)
& ? [X6: $i] :
( '$ki_exists_in_world_$i'(X5,X6)
& p(X5,X6) ) ) ) ),
inference(rectify,[],[f10]) ).
tff(f14,plain,
! [X0: '$ki_world',X1: '$ki_world',X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_accessible'(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
tff(f15,plain,
! [X0: '$ki_world',X1: '$ki_world',X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_accessible'(X0,X1) ),
inference(flattening,[],[f14]) ).
tff(f23,plain,
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X5)
| ! [X6: $i] :
( ~ '$ki_exists_in_world_$i'(X5,X6)
| ~ p(X5,X6) ) )
& ? [X3: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
& ? [X4: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X4)
& p(X4,X3) ) )
& ! [X0: $i] :
( ! [X1: '$ki_world'] :
( ? [X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
& qmltpeq(X1,X0,X2) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f24,plain,
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X5)
| ! [X6: $i] :
( ~ '$ki_exists_in_world_$i'(X5,X6)
| ~ p(X5,X6) ) )
& ? [X3: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
& ? [X4: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X4)
& p(X4,X3) ) )
& ! [X0: $i] :
( ! [X1: '$ki_world'] :
( ? [X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
& qmltpeq(X1,X0,X2) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ) ),
inference(flattening,[],[f23]) ).
tff(f26,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ p(X0,X1) ) )
& ? [X2: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X2)
& ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& p(X3,X2) ) )
& ! [X4: $i] :
( ! [X5: '$ki_world'] :
( ? [X6: $i] :
( '$ki_exists_in_world_$i'(X5,X6)
& qmltpeq(X5,X4,X6) )
| ~ '$ki_accessible'('$ki_local_world',X5) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X4) ) ),
inference(rectify,[],[f24]) ).
tff(f27,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ p(X0,X1) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK1)
& '$ki_accessible'('$ki_local_world',sK2)
& p(sK2,sK1)
& ! [X4: $i] :
( ! [X5: '$ki_world'] :
( ( '$ki_exists_in_world_$i'(X5,sK3(X4,X5))
& qmltpeq(X5,X4,sK3(X4,X5)) )
| ~ '$ki_accessible'('$ki_local_world',X5) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1),skolemize(X3,sK2),skolemize(X6,sK3(X4,X5))],[f26]) ).
tff(f30,plain,
! [X2: $i,X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| '$ki_exists_in_world_$i'(X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tff(f38,plain,
p(sK2,sK1),
inference(cnf_transformation,[],[f27]) ).
tff(f39,plain,
'$ki_accessible'('$ki_local_world',sK2),
inference(cnf_transformation,[],[f27]) ).
tff(f40,plain,
'$ki_exists_in_world_$i'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f27]) ).
tff(f41,plain,
! [X0: '$ki_world',X1: $i] :
( ~ p(X0,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f27]) ).
tff(f42,plain,
( ~ '$ki_exists_in_world_$i'(sK2,sK1)
| ~ '$ki_accessible'('$ki_local_world',sK2) ),
inference(resolution,[],[f41,f38]) ).
tff(f44,definition,
( spl4_1
<=> '$ki_accessible'('$ki_local_world',sK2) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f45,plain,
( ~ '$ki_accessible'('$ki_local_world',sK2)
| spl4_1 ),
inference(avatar_component_clause,[],[f44]) ).
tff(f47,definition,
( spl4_2
<=> '$ki_exists_in_world_$i'(sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f48,plain,
( ~ '$ki_exists_in_world_$i'(sK2,sK1)
| spl4_2 ),
inference(avatar_component_clause,[],[f47]) ).
tff(f49,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f42,f47,f44]) ).
tff(f50,plain,
( $false
| spl4_1 ),
inference(resolution,[],[f45,f39]) ).
tff(f51,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f50]) ).
tff(f55,plain,
! [X0: $i] :
( '$ki_exists_in_world_$i'(sK2,X0)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
inference(resolution,[],[f30,f39]) ).
tff(f58,plain,
( ~ '$ki_exists_in_world_$i'('$ki_local_world',sK1)
| spl4_2 ),
inference(resolution,[],[f55,f48]) ).
tff(f59,plain,
( $false
| spl4_2 ),
inference(resolution,[],[f58,f40]) ).
tff(f60,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f59]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s2,plain,
spl4_1,
inference(sat_conversion,[],[f51]) ).
cnf(s3,plain,
spl4_2,
inference(sat_conversion,[],[f60]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
tff(f61,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO891_16 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n001.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 18:46:04 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.21/0.88 % (607913)Detected formulas, will run a generic FOF schedule.
% 2.21/0.88 % (607962)dis-21_1_sil=8000:lcm=predicate:random_seed=2410088218:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 2.21/0.88 % (607962)First to succeed.
% 2.21/0.88 % (607962)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-607913"
% 2.21/0.88 % (607961)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2810473301:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 2.21/0.88 % (607959)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=880960871:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 2.21/0.88 % (607958)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=3618017169:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 2.21/0.88 % (607957)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=3418948909:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 2.21/0.88 % (607956)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=1832946888:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 2.21/0.88 % (607960)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2500311347:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 2.21/0.88 % (607960)Also succeeded, but the first one will report.
% 2.21/0.88 % (607959)Also succeeded, but the first one will report.
% 2.21/0.88 % (607961)Also succeeded, but the first one will report.
% 2.21/0.88 % (607962)Refutation found. Thanks to Tanya!
% 2.21/0.88 % SZS status Theorem for theBenchmark
% 2.21/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 2.21/0.88 % (607962)------------------------------
% 2.21/0.88 % (607962)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.21/0.88 % (607962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.88 % (607962)CaDiCaL version: 2.1.3
% 2.21/0.88 % (607962)Termination reason: Refutation
% 2.21/0.88 % (607962)Time elapsed: 0.002 s
% 2.21/0.88 % (607962)Peak memory usage: 89 MB
% 2.21/0.88 % (607962)Instructions burned: 2 (million)
% 2.21/0.88 % (607962)------------------------------
% 2.21/0.88 % (607962)------------------------------
% 2.21/0.88 % (607913)Success in time 0.249 s
% 2.21/0.88 % Vampire exiting
%------------------------------------------------------------------------------