%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO890_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 : n016.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 3.66s 1.26s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 78 ( 27 ~; 17 |; 21 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 42 ( 30 !; 12 ?; 42 :)
% 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' ).
tff(func_def_3,type,
sK2: '$ki_world' > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
e: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
f: ( '$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(f5,conjecture,
( ? [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( e(X1,X0)
& f(X1,X0) ) ) )
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ? [X0: $i] :
( '$ki_exists_in_world_$i'(X1,X0)
& f(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f6,negated_conjecture,
~ ( ? [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( e(X1,X0)
& f(X1,X0) ) ) )
=> ! [X1: '$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)],[f5]) ).
tff(f7,plain,
~ ( ? [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( e(X1,X0)
& f(X1,X0) ) ) )
=> ! [X2: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X2)
=> ? [X3: $i] :
( '$ki_exists_in_world_$i'(X2,X3)
& f(X2,X3) ) ) ),
inference(rectify,[],[f6]) ).
tff(f8,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_$i'(X2,X3)
& f(X2,X3) ) ) ),
inference(pure_predicate_removal,[],[f7]) ).
tff(f9,plain,
( ? [X2: '$ki_world'] :
( ! [X3: $i] :
( ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ f(X2,X3) )
& '$ki_accessible'('$ki_local_world',X2) )
& ? [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( f(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1) ) ) ),
inference(ennf_transformation,[],[f8]) ).
tff(f12,plain,
! [X0: '$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(f13,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,[],[f12]) ).
tff(f14,plain,
( ? [X0: '$ki_world'] :
( ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ f(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) )
& ? [X2: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X2)
& ! [X3: '$ki_world'] :
( f(X3,X2)
| ~ '$ki_accessible'('$ki_local_world',X3) ) ) ),
inference(rectify,[],[f9]) ).
tff(f15,plain,
( ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X1)
| ~ f(sK0,X1) )
& '$ki_accessible'('$ki_local_world',sK0)
& '$ki_exists_in_world_$i'('$ki_local_world',sK1)
& ! [X3: '$ki_world'] :
( f(X3,sK1)
| ~ '$ki_accessible'('$ki_local_world',X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1)],[f14]) ).
tff(f17,plain,
! [X3: '$ki_world'] :
( f(X3,sK1)
| ~ '$ki_accessible'('$ki_local_world',X3) ),
inference(cnf_transformation,[],[f15]) ).
tff(f18,plain,
'$ki_exists_in_world_$i'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f15]) ).
tff(f19,plain,
'$ki_accessible'('$ki_local_world',sK0),
inference(cnf_transformation,[],[f15]) ).
tff(f20,plain,
! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X1)
| ~ f(sK0,X1) ),
inference(cnf_transformation,[],[f15]) ).
tff(f24,plain,
! [X2: $i,X0: '$ki_world',X1: '$ki_world'] :
( '$ki_exists_in_world_$i'(X1,X2)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_accessible'(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
tff(f26,plain,
! [X0: '$ki_world',X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'(X0,sK0)
| ~ f(sK0,X1) ),
inference(resolution,[],[f24,f20]) ).
tff(f27,plain,
( ~ '$ki_accessible'('$ki_local_world',sK0)
| ~ f(sK0,sK1) ),
inference(resolution,[],[f26,f18]) ).
tff(f30,plain,
~ '$ki_accessible'('$ki_local_world',sK0),
inference(forward_subsumption_resolution,[],[f27,f17]) ).
tff(f31,plain,
$false,
inference(forward_subsumption_resolution,[],[f30,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO890_16 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n016.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Mon Sep 28 18:45:03 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 Running first-order theorem proving
% 0.09/0.18 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
% 3.66/1.26 % (3863358)Detected formulas, will run a generic FOF schedule.
% 3.66/1.26 % (3863440)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=25034259:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.66/1.26 % (3863445)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3715726076:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.66/1.26 % (3863446)dis-21_1_sil=8000:lcm=predicate:random_seed=2468308365: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)
% 3.66/1.26 % (3863442)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=285932604:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.66/1.26 % (3863437)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=1439677798:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.66/1.26 % (3863443)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2651729190:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.66/1.26 % (3863439)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=2296621763:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.66/1.26 % (3863443)First to succeed.
% 3.66/1.26 % (3863442)Also succeeded, but the first one will report.
% 3.66/1.26 % (3863445)Also succeeded, but the first one will report.
% 3.66/1.26 % (3863446)Also succeeded, but the first one will report.
% 3.66/1.26 % (3863443)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3863358"
% 3.66/1.26 % (3863443)Refutation found. Thanks to Tanya!
% 3.66/1.26 % SZS status Theorem for theBenchmark
% 3.66/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.26 % (3863443)------------------------------
% 3.66/1.26 % (3863443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.26 % (3863443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.26 % (3863443)CaDiCaL version: 2.1.3
% 3.66/1.26 % (3863443)Termination reason: Refutation
% 3.66/1.26 % (3863443)Time elapsed: 0.002 s
% 3.66/1.26 % (3863443)Peak memory usage: 88 MB
% 3.66/1.26 % (3863443)Instructions burned: 1 (million)
% 3.66/1.26 % (3863443)------------------------------
% 3.66/1.26 % (3863443)------------------------------
% 3.66/1.26 % (3863358)Success in time 0.438 s
% 3.66/1.26 % Vampire exiting
%------------------------------------------------------------------------------