%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL961_11 : 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 : n018.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 11:57:19 AM UTC 2026
% Result : Theorem 3.62s 1.42s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 84 ( 20 ~; 12 |; 28 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 44 ( 32 !; 12 ?; 44 :)
% 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_2,type,
sK1: '$ki_world' ).
tff(func_def_3,type,
sK2: '$ki_world' ).
tff(func_def_4,type,
sK3: '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
p: '$ki_world' > $o ).
tff(pred_def_3,type,
q: '$ki_world' > $o ).
tff(f1,axiom,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
tff(f2,conjecture,
( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> p(X1) )
=> ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> q(X1) ) ) )
| ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> q(X1) )
=> ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> p(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f3,negated_conjecture,
~ ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> p(X1) )
=> ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> q(X1) ) ) )
| ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> q(X1) )
=> ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> p(X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
~ ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> p(X1) )
=> ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> q(X2) ) ) )
| ! [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
=> ( ! [X4: '$ki_world'] :
( '$ki_accessible'(X3,X4)
=> q(X4) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
=> p(X5) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f5,plain,
( ? [X0: '$ki_world'] :
( ? [X2: '$ki_world'] :
( ~ q(X2)
& '$ki_accessible'(X0,X2) )
& ! [X1: '$ki_world'] :
( p(X1)
| ~ '$ki_accessible'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) )
& ? [X3: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X3,X5) )
& ! [X4: '$ki_world'] :
( q(X4)
| ~ '$ki_accessible'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
( ? [X0: '$ki_world'] :
( ? [X2: '$ki_world'] :
( ~ q(X2)
& '$ki_accessible'(X0,X2) )
& ! [X1: '$ki_world'] :
( p(X1)
| ~ '$ki_accessible'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) )
& ? [X3: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X3,X5) )
& ! [X4: '$ki_world'] :
( q(X4)
| ~ '$ki_accessible'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) ) ),
inference(flattening,[],[f5]) ).
tff(f7,plain,
( ? [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( ~ q(X1)
& '$ki_accessible'(X0,X1) )
& ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X0,X2) )
& '$ki_accessible'('$ki_local_world',X0) )
& ? [X3: '$ki_world'] :
( ? [X4: '$ki_world'] :
( ~ p(X4)
& '$ki_accessible'(X3,X4) )
& ! [X5: '$ki_world'] :
( q(X5)
| ~ '$ki_accessible'(X3,X5) )
& '$ki_accessible'('$ki_local_world',X3) ) ),
inference(rectify,[],[f6]) ).
tff(f8,plain,
( ~ q(sK1)
& '$ki_accessible'(sK0,sK1)
& ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(sK0,X2) )
& '$ki_accessible'('$ki_local_world',sK0)
& ~ p(sK3)
& '$ki_accessible'(sK2,sK3)
& ! [X5: '$ki_world'] :
( q(X5)
| ~ '$ki_accessible'(sK2,X5) )
& '$ki_accessible'('$ki_local_world',sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2),skolemize(X4,sK3)],[f7]) ).
tff(f10,plain,
! [X5: '$ki_world'] :
( q(X5)
| ~ '$ki_accessible'(sK2,X5) ),
inference(cnf_transformation,[],[f8]) ).
tff(f16,plain,
~ q(sK1),
inference(cnf_transformation,[],[f8]) ).
tff(f17,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f1]) ).
tff(f18,plain,
! [X5: '$ki_world'] : q(X5),
inference(forward_subsumption_resolution,[],[f10,f17]) ).
tff(f20,plain,
$false,
inference(resolution,[],[f18,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL961_11 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n018.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 17:11:08 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.62/1.42 % (2602359)Detected formulas, will run a generic FOF schedule.
% 3.62/1.42 % (2602461)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=245109337:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.62/1.42 % (2602464)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=662002505:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.62/1.42 % (2602462)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1451237331:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.62/1.42 % (2602459)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=3418551888:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.62/1.42 % (2602465)dis-21_1_sil=8000:lcm=predicate:random_seed=2348187018: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)
% 3.62/1.42 % (2602460)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=1973782531:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.62/1.42 % (2602463)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3578696222:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.62/1.42 % (2602463)Also succeeded, but the first one will report.
% 3.62/1.42 % (2602465)Also succeeded, but the first one will report.
% 3.62/1.42 % (2602462)First to succeed.
% 3.62/1.42 % (2602464)Also succeeded, but the first one will report.
% 3.62/1.42 % (2602462)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2602359"
% 3.62/1.42 % (2602462)Refutation found. Thanks to Tanya!
% 3.62/1.42 % SZS status Theorem for theBenchmark
% 3.62/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.42 % (2602462)------------------------------
% 3.62/1.42 % (2602462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.42 % (2602462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.42 % (2602462)CaDiCaL version: 2.1.3
% 3.62/1.42 % (2602462)Termination reason: Refutation
% 3.62/1.42 % (2602462)Time elapsed: 0.002 s
% 3.62/1.42 % (2602462)Peak memory usage: 88 MB
% 3.62/1.42 % (2602462)Instructions burned: 1 (million)
% 3.62/1.42 % (2602462)------------------------------
% 3.62/1.42 % (2602462)------------------------------
% 3.62/1.42 % (2602359)Success in time 0.439 s
% 3.62/1.42 % Vampire exiting
%------------------------------------------------------------------------------