%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n011.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 11:57:20 AM UTC 2026
% Result : Theorem 3.99s 1.38s
% Output : Refutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 104 ( 47 ~; 39 |; 5 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 39 ( 36 !; 3 ?; 39 :)
% 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' ).
tff(func_def_4,type,
sK1: '$ki_world' > '$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'] :
( '$ki_accessible'('#idx(b)',X1,X2)
=> p(X2) ) ) ),
inference(rectify,[],[f6]) ).
tff(f11,plain,
? [X0: '$ki_world'] :
( p(X0)
& '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f12,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(f13,plain,
! [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( p(X1)
| ~ '$ki_accessible'('#idx(b)',X0,X1) )
| ~ p(X0)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
inference(ennf_transformation,[],[f5]) ).
tff(f14,plain,
! [X0: '$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,[],[f13]) ).
tff(f19,plain,
( p(sK0)
& '$ki_accessible'('#idx(a)','$ki_local_world',sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f11]) ).
tff(f20,plain,
( ! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( ~ p(X1)
& '$ki_accessible'('#idx(b)',X0,X1) )
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) )
| ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2) ) ),
inference(rectify,[],[f12]) ).
tff(f21,plain,
( ! [X0: '$ki_world'] :
( ( ~ p(sK1(X0))
& '$ki_accessible'('#idx(b)',X0,sK1(X0)) )
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) )
| ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f20]) ).
tff(f22,plain,
'$ki_accessible'('#idx(a)','$ki_local_world',sK0),
inference(cnf_transformation,[],[f19]) ).
tff(f23,plain,
p(sK0),
inference(cnf_transformation,[],[f19]) ).
tff(f24,plain,
~ p('$ki_local_world'),
inference(cnf_transformation,[],[f7]) ).
tff(f25,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X0,sK1(X0))
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
| p(X2)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2) ),
inference(cnf_transformation,[],[f21]) ).
tff(f26,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
| p(X2)
| ~ p(sK1(X0)) ),
inference(cnf_transformation,[],[f21]) ).
tff(f27,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)',X0,X1)
| p(X1)
| ~ p(X0)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
inference(cnf_transformation,[],[f14]) ).
tff(f31,plain,
! [X0: '$ki_world'] : '$ki_accessible'('#idx(b)',X0,X0),
inference(cnf_transformation,[],[f3]) ).
tff(f40,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
| p(X1)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X1)
| p(sK1(X0))
| ~ p(X0)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
inference(resolution,[],[f25,f27]) ).
tff(f42,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
| p(X1)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X1)
| p(sK1(X0))
| ~ p(X0) ),
inference(duplicate_literal_removal,[],[f40]) ).
tff(f43,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X1)
| p(X1)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
| ~ p(X0) ),
inference(forward_subsumption_resolution,[],[f42,f26]) ).
tff(f44,plain,
! [X0: '$ki_world'] :
( p('$ki_local_world')
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
| ~ p(X0) ),
inference(resolution,[],[f43,f31]) ).
tff(f47,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
| ~ p(X0) ),
inference(forward_subsumption_resolution,[],[f44,f24]) ).
tff(f48,plain,
~ p(sK0),
inference(resolution,[],[f47,f22]) ).
tff(f51,plain,
$false,
inference(forward_subsumption_resolution,[],[f48,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL962_16 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 17:08:45 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 3.99/1.38 % (2631099)Detected formulas, will run a generic FOF schedule.
% 3.99/1.38 % (2631115)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1803930301:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.99/1.38 % (2631117)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3032566793:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.99/1.38 % (2631118)dis-21_1_sil=8000:lcm=predicate:random_seed=886570764: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)
% 3.99/1.38 % (2631112)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=2486774153:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.99/1.38 % (2631116)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=523705510:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.99/1.38 % (2631113)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=293510934:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.99/1.38 % (2631111)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=4139449974:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.99/1.38 % (2631115)Refutation not found, incomplete strategy
% 3.99/1.38 % (2631115)------------------------------
% 3.99/1.38 % (2631115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.38 % (2631115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.38 % (2631115)CaDiCaL version: 2.1.3
% 3.99/1.38 % (2631115)Termination reason: Refutation not found, incomplete strategy
% 3.99/1.38 % (2631115)Time elapsed: 0.001 s
% 3.99/1.38 % (2631115)Peak memory usage: 87 MB
% 3.99/1.38 % (2631116)First to succeed.
% 3.99/1.38 % (2631118)Also succeeded, but the first one will report.
% 3.99/1.38 % (2631117)Also succeeded, but the first one will report.
% 3.99/1.38 % (2631116)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2631099"
% 3.99/1.38 % (2631115)------------------------------
% 3.99/1.38 % (2631115)------------------------------
% 3.99/1.38 % (2631116)Refutation found. Thanks to Tanya!
% 3.99/1.38 % SZS status Theorem for theBenchmark
% 3.99/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.99/1.38 % (2631116)------------------------------
% 3.99/1.38 % (2631116)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.38 % (2631116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.38 % (2631116)CaDiCaL version: 2.1.3
% 3.99/1.38 % (2631116)Termination reason: Refutation
% 3.99/1.38 % (2631116)Time elapsed: 0.002 s
% 3.99/1.38 % (2631116)Peak memory usage: 88 MB
% 3.99/1.38 % (2631116)Instructions burned: 1 (million)
% 3.99/1.38 % (2631116)------------------------------
% 3.99/1.38 % (2631116)------------------------------
% 3.99/1.38 % (2631099)Success in time 0.517 s
% 3.99/1.38 % Vampire exiting
%------------------------------------------------------------------------------