%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO894_8 : 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 : n017.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 02:29:18 PM UTC 2026
% Result : Theorem 2.81s 1.16s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 7 unt; 0 typ; 7 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 193 ( 86 ~; 74 |; 15 &)
% ( 10 <=>; 6 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 3 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 : 10 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 28 ( 0 sgn 21 !; 7 ?; 27 :)
% 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: '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
p: '$ki_world' > $o ).
tff(f2,conjecture,
( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
=> ~ p(X0) ) )
<=> ~ ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& p(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f3,negated_conjecture,
~ ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
=> ~ p(X0) ) )
<=> ~ ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& p(X0) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
~ ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
=> ~ p(X0) ) )
<=> ~ ? [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
& p(X1) ) ),
inference(rectify,[],[f3]) ).
tff(f5,plain,
( ! [X0: '$ki_world'] :
( ~ p(X0)
| ~ p(X0)
| ~ '$ki_accessible'('$ki_local_world',X0) )
<~> ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ p(X1) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
( ! [X0: '$ki_world'] :
( ~ p(X0)
| ~ p(X0)
| ~ '$ki_accessible'('$ki_local_world',X0) )
<~> ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ p(X1) ) ),
inference(flattening,[],[f5]) ).
tff(f7,plain,
( ( ? [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
& p(X1) )
| ? [X0: '$ki_world'] :
( p(X0)
& p(X0)
& '$ki_accessible'('$ki_local_world',X0) ) )
& ( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ p(X1) )
| ! [X0: '$ki_world'] :
( ~ p(X0)
| ~ p(X0)
| ~ '$ki_accessible'('$ki_local_world',X0) ) ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f8,plain,
( ( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& p(X0) )
| ? [X1: '$ki_world'] :
( p(X1)
& p(X1)
& '$ki_accessible'('$ki_local_world',X1) ) )
& ( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ p(X2) )
| ! [X3: '$ki_world'] :
( ~ p(X3)
| ~ p(X3)
| ~ '$ki_accessible'('$ki_local_world',X3) ) ) ),
inference(rectify,[],[f7]) ).
tff(f9,plain,
( ( ( '$ki_accessible'('$ki_local_world',sK0)
& p(sK0) )
| ( p(sK1)
& p(sK1)
& '$ki_accessible'('$ki_local_world',sK1) ) )
& ( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ p(X2) )
| ! [X3: '$ki_world'] :
( ~ p(X3)
| ~ p(X3)
| ~ '$ki_accessible'('$ki_local_world',X3) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
tff(f10,plain,
! [X2: '$ki_world',X3: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ p(X2)
| ~ p(X3)
| ~ p(X3)
| ~ '$ki_accessible'('$ki_local_world',X3) ),
inference(cnf_transformation,[],[f9]) ).
tff(f11,plain,
( p(sK0)
| '$ki_accessible'('$ki_local_world',sK1) ),
inference(cnf_transformation,[],[f9]) ).
tff(f13,plain,
( p(sK0)
| p(sK1) ),
inference(cnf_transformation,[],[f9]) ).
tff(f14,plain,
( '$ki_accessible'('$ki_local_world',sK0)
| '$ki_accessible'('$ki_local_world',sK1) ),
inference(cnf_transformation,[],[f9]) ).
tff(f16,plain,
( '$ki_accessible'('$ki_local_world',sK0)
| p(sK1) ),
inference(cnf_transformation,[],[f9]) ).
tff(f18,plain,
! [X2: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ p(X2)
| sP2 ),
inference(cnf_transformation,[],[f18_D]) ).
tff(f18_D,definition,
( ! [X2] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ p(X2) )
<=> ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP2])],[general_splitting_component_introduction]) ).
tff(f19,plain,
! [X3: '$ki_world'] :
( ~ p(X3)
| ~ p(X3)
| ~ '$ki_accessible'('$ki_local_world',X3)
| ~ sP2 ),
inference(general_splitting,[],[f10,f18_D]) ).
tff(f20,plain,
! [X3: '$ki_world'] :
( ~ p(X3)
| ~ '$ki_accessible'('$ki_local_world',X3)
| ~ sP2 ),
inference(duplicate_literal_removal,[],[f19]) ).
tff(f22,definition,
( spl3_1
<=> '$ki_accessible'('$ki_local_world',sK1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f24,plain,
( '$ki_accessible'('$ki_local_world',sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f22]) ).
tff(f26,definition,
( spl3_2
<=> p(sK0) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f28,plain,
( p(sK0)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f26]) ).
tff(f29,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f11,f26,f22]) ).
tff(f31,definition,
( spl3_3
<=> p(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f33,plain,
( p(sK1)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f31]) ).
tff(f35,plain,
( spl3_3
| spl3_2 ),
inference(avatar_split_clause,[],[f13,f26,f31]) ).
tff(f37,definition,
( spl3_4
<=> '$ki_accessible'('$ki_local_world',sK0) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f39,plain,
( '$ki_accessible'('$ki_local_world',sK0)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f37]) ).
tff(f40,plain,
( spl3_1
| spl3_4 ),
inference(avatar_split_clause,[],[f14,f37,f22]) ).
tff(f42,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f16,f37,f31]) ).
tff(f44,definition,
( spl3_5
<=> sP2 ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
tff(f48,definition,
( spl3_6
<=> ! [X2: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ p(X2) ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
tff(f49,plain,
( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ p(X2) )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f48]) ).
tff(f50,plain,
( spl3_5
| spl3_6 ),
inference(avatar_split_clause,[],[f18,f48,f44]) ).
tff(f51,plain,
( ~ spl3_5
| spl3_6 ),
inference(avatar_split_clause,[],[f20,f48,f44]) ).
tff(f52,plain,
( ~ p(sK0)
| ~ spl3_4
| ~ spl3_6 ),
inference(resolution,[],[f49,f39]) ).
tff(f54,plain,
( $false
| ~ spl3_2
| ~ spl3_4
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f52,f28]) ).
tff(f55,plain,
( ~ spl3_2
| ~ spl3_4
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f54]) ).
tff(f56,plain,
( ~ p(sK1)
| ~ spl3_1
| ~ spl3_6 ),
inference(resolution,[],[f24,f49]) ).
tff(f57,plain,
( $false
| ~ spl3_1
| ~ spl3_3
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f56,f33]) ).
tff(f58,plain,
( ~ spl3_1
| ~ spl3_3
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f57]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f29]) ).
cnf(s3,plain,
( spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f35]) ).
cnf(s4,plain,
( spl3_1
| spl3_4 ),
inference(sat_conversion,[],[f40]) ).
cnf(s6,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f42]) ).
cnf(s7,plain,
( spl3_5
| spl3_6 ),
inference(sat_conversion,[],[f50]) ).
cnf(s8,plain,
( ~ spl3_5
| spl3_6 ),
inference(sat_conversion,[],[f51]) ).
cnf(s9,plain,
( ~ spl3_2
| ~ spl3_4
| ~ spl3_6 ),
inference(sat_conversion,[],[f55]) ).
cnf(s10,plain,
( ~ spl3_1
| ~ spl3_3
| ~ spl3_6 ),
inference(sat_conversion,[],[f58]) ).
cnf(s11,plain,
spl3_6,
inference(rat,[],[s7,s8]) ).
cnf(s12,plain,
spl3_1,
inference(rat,[],[s9,s1,s4,s11]) ).
cnf(s13,plain,
~ spl3_3,
inference(rat,[],[s10,s11,s12]) ).
cnf(s14,plain,
spl3_4,
inference(rat,[],[s6,s13]) ).
cnf(s15,plain,
spl3_2,
inference(rat,[],[s3,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s9,s11,s14,s15]) ).
tff(f59,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO894_8 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n017.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Mon Sep 28 18:35:36 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running first-order theorem proving
% 0.11/0.22 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
% 2.81/1.16 % (3854564)Detected formulas, will run a generic FOF schedule.
% 2.81/1.16 % (3854681)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=116695114:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.81/1.16 % (3854681)First to succeed.
% 2.81/1.16 % (3854681)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3854564"
% 2.81/1.16 % (3854683)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4190388616:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.81/1.16 % (3854684)dis-21_1_sil=8000:lcm=predicate:random_seed=2194078061: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)
% 2.81/1.16 % (3854679)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=1728040765:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.81/1.16 % (3854680)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=1283499933:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.81/1.16 % (3854678)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=1366886188:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.81/1.16 % (3854682)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1042157859:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.81/1.16 % (3854682)Also succeeded, but the first one will report.
% 2.81/1.16 % (3854684)Also succeeded, but the first one will report.
% 2.81/1.16 % (3854683)Also succeeded, but the first one will report.
% 2.81/1.16 % (3854681)Refutation found. Thanks to Tanya!
% 2.81/1.16 % SZS status Theorem for theBenchmark
% 2.81/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.81/1.16 % (3854681)------------------------------
% 2.81/1.16 % (3854681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.16 % (3854681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.16 % (3854681)CaDiCaL version: 2.1.3
% 2.81/1.16 % (3854681)Termination reason: Refutation
% 2.81/1.16 % (3854681)Time elapsed: 0.002 s
% 2.81/1.16 % (3854681)Peak memory usage: 89 MB
% 2.81/1.16 % (3854681)Instructions burned: 1 (million)
% 2.81/1.16 % (3854681)------------------------------
% 2.81/1.16 % (3854681)------------------------------
% 2.81/1.16 % (3854564)Success in time 0.306 s
% 2.81/1.16 % Vampire exiting
%------------------------------------------------------------------------------