%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO893_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 : n015.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 3.47s 1.26s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 6 unt; 0 typ; 1 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 175 ( 67 ~; 52 |; 41 &)
% ( 4 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-1 aty)
% Number of variables : 81 ( 52 !; 29 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_1,type,
sK1: '$ki_world' > '$ki_world' ).
tff(func_def_2,type,
sK2: '$ki_world' ).
tff(func_def_3,type,
sK3: '$ki_world' > '$ki_world' ).
tff(func_def_4,type,
sK4: '$ki_world' > '$ki_world' ).
tff(func_def_5,type,
sK5: '$ki_world' ).
tff(func_def_6,type,
sK6: '$ki_world' > '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
p: '$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'] :
( '$ki_accessible'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X1,X2)
=> p(X2) ) ) )
<=> ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> ? [X2: '$ki_world'] :
( '$ki_accessible'(X1,X2)
& ~ p(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f3,negated_conjecture,
~ ( ~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X1,X2)
=> p(X2) ) ) )
<=> ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> ? [X2: '$ki_world'] :
( '$ki_accessible'(X1,X2)
& ~ p(X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
~ ( ~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X1,X2)
=> p(X2) ) ) )
<=> ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( '$ki_accessible'(X3,X4)
=> ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f5,plain,
( ? [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) )
& '$ki_accessible'('$ki_local_world',X0) )
<~> ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(X3,X4) ) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,definition,
( sP0
<=> ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(X3,X4) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f7,plain,
( ? [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) )
& '$ki_accessible'('$ki_local_world',X0) )
<~> sP0 ),
inference(definition_folding,[],[f5,f6]) ).
tff(f8,plain,
( ( sP0
| ! [X3: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X3)
| ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| p(X5) )
& '$ki_accessible'(X3,X4) ) ) )
& ( ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(X3,X4) ) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f9,plain,
( ( sP0
| ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ? [X1: '$ki_world'] :
( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X1,X2)
| p(X2) )
& '$ki_accessible'(X0,X1) ) ) )
& ( ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(X3,X4) ) )
| ~ sP0 ) ),
inference(rectify,[],[f8]) ).
tff(f10,plain,
( ( sP0
| ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(sK1(X0),X2)
| p(X2) )
& '$ki_accessible'(X0,sK1(X0)) ) ) )
& ( ( '$ki_accessible'('$ki_local_world',sK2)
& ! [X4: '$ki_world'] :
( ( '$ki_accessible'(X4,sK3(X4))
& ~ p(sK3(X4)) )
| ~ '$ki_accessible'(sK2,X4) ) )
| ~ sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X1,sK1(X0)),skolemize(X3,sK2),skolemize(X5,sK3(X4))],[f9]) ).
tff(f11,plain,
( ( ~ sP0
| ! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
& ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) )
& ( sP0
| ? [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) )
& '$ki_accessible'('$ki_local_world',X0) ) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f12,plain,
( ( ~ sP0
| ! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
& ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) )
& ( sP0
| ? [X3: '$ki_world'] :
( ! [X4: '$ki_world'] :
( ~ '$ki_accessible'(X3,X4)
| ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) ) )
& '$ki_accessible'('$ki_local_world',X3) ) ) ),
inference(rectify,[],[f11]) ).
tff(f13,plain,
( ( ~ sP0
| ! [X0: '$ki_world'] :
( ( '$ki_accessible'(X0,sK4(X0))
& ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(sK4(X0),X2) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) )
& ( sP0
| ( ! [X4: '$ki_world'] :
( ~ '$ki_accessible'(sK5,X4)
| ( ~ p(sK6(X4))
& '$ki_accessible'(X4,sK6(X4)) ) )
& '$ki_accessible'('$ki_local_world',sK5) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X1,sK4(X0)),skolemize(X3,sK5),skolemize(X5,sK6(X4))],[f12]) ).
tff(f14,plain,
! [X4: '$ki_world'] :
( ~ p(sK3(X4))
| ~ '$ki_accessible'(sK2,X4)
| ~ sP0 ),
inference(cnf_transformation,[],[f10]) ).
tff(f18,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( sP0
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(sK1(X0),X2)
| p(X2) ),
inference(cnf_transformation,[],[f10]) ).
tff(f21,plain,
! [X4: '$ki_world'] :
( ~ p(sK6(X4))
| ~ '$ki_accessible'(sK5,X4)
| sP0 ),
inference(cnf_transformation,[],[f13]) ).
tff(f22,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ '$ki_accessible'(sK4(X0),X2)
| p(X2)
| ~ sP0
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f13]) ).
tff(f24,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f1]) ).
tff(f28,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( p(X0)
| ~ sP0
| ~ '$ki_accessible'('$ki_local_world',X1) ),
inference(resolution,[],[f24,f22]) ).
tff(f29,plain,
! [X0: '$ki_world'] :
( p(X0)
| ~ sP0 ),
inference(forward_subsumption_resolution,[],[f28,f24]) ).
tff(f31,plain,
! [X4: '$ki_world'] :
( ~ '$ki_accessible'(sK2,X4)
| ~ sP0 ),
inference(forward_subsumption_resolution,[],[f14,f29]) ).
tff(f32,plain,
~ sP0,
inference(forward_subsumption_resolution,[],[f31,f24]) ).
tff(f33,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(sK1(X0),X2)
| p(X2) ),
inference(forward_subsumption_resolution,[],[f18,f29]) ).
tff(f34,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ '$ki_accessible'(sK1(X0),X2)
| p(X2) ),
inference(forward_subsumption_resolution,[],[f33,f24]) ).
tff(f35,plain,
! [X2: '$ki_world'] : p(X2),
inference(forward_subsumption_resolution,[],[f34,f24]) ).
tff(f36,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK5,X0)
| sP0 ),
inference(resolution,[],[f35,f21]) ).
tff(f37,plain,
! [X0: '$ki_world'] : ~ '$ki_accessible'(sK5,X0),
inference(forward_subsumption_resolution,[],[f36,f32]) ).
tff(f38,plain,
$false,
inference(forward_subsumption_resolution,[],[f37,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO893_11 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n015.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 18:43:17 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 3.47/1.26 % (2879387)Detected formulas, will run a generic FOF schedule.
% 3.47/1.26 % (2879473)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=423972762:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 3.47/1.26 % (2879471)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=966750075:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 3.47/1.26 % (2879479)dis-21_1_sil=8000:lcm=predicate:random_seed=2610783000: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)
% 3.47/1.26 % (2879474)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=3925793571:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 3.47/1.26 % (2879475)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2569302468:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 3.47/1.26 % (2879476)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3876823238:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 3.47/1.26 % (2879476)First to succeed.
% 3.47/1.26 % (2879475)Refutation not found, incomplete strategy
% 3.47/1.26 % (2879475)------------------------------
% 3.47/1.26 % (2879475)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.26 % (2879475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.26 % (2879475)CaDiCaL version: 2.1.3
% 3.47/1.26 % (2879475)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.26 % (2879475)Time elapsed: 0.001 s
% 3.47/1.26 % (2879475)Peak memory usage: 88 MB
% 3.47/1.26 % (2879475)Instructions burned: 1 (million)
% 3.47/1.26 % (2879479)Also succeeded, but the first one will report.
% 3.47/1.26 % (2879476)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2879387"
% 3.47/1.26 % (2879478)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2924030844:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 3.47/1.26 % (2879478)Also succeeded, but the first one will report.
% 3.47/1.26 % (2879475)------------------------------
% 3.47/1.26 % (2879475)------------------------------
% 3.47/1.26 % (2879476)Refutation found. Thanks to Tanya!
% 3.47/1.26 % SZS status Theorem for theBenchmark
% 3.47/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.26 % (2879476)------------------------------
% 3.47/1.26 % (2879476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.26 % (2879476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.26 % (2879476)CaDiCaL version: 2.1.3
% 3.47/1.26 % (2879476)Termination reason: Refutation
% 3.47/1.26 % (2879476)Time elapsed: 0.002 s
% 3.47/1.26 % (2879476)Peak memory usage: 88 MB
% 3.47/1.26 % (2879476)Instructions burned: 1 (million)
% 3.47/1.26 % (2879476)------------------------------
% 3.47/1.26 % (2879476)------------------------------
% 3.47/1.26 % (2879387)Success in time 0.391 s
% 3.47/1.26 % Vampire exiting
%------------------------------------------------------------------------------