%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO889_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 : 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 02:29:16 PM UTC 2026
% Result : Theorem 0.17s 1.20s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 168 ( 63 ~; 49 |; 44 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 14 ( 14 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 72 ( 45 !; 27 ?; 72 :)
% 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' > $i ).
tff(func_def_2,type,
sK1: '$ki_world' ).
tff(func_def_4,type,
sK3: ( '$ki_world' * $i ) > '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
a: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
b: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f5,conjecture,
( ( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> a(X2,X1) ) ) )
& ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
& b(X2,X1) ) ) ) )
=> ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ? [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
& a(X2,X1)
& b(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f6,negated_conjecture,
~ ( ( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> a(X2,X1) ) ) )
& ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
& b(X2,X1) ) ) ) )
=> ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ? [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
& a(X2,X1)
& b(X2,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f7,plain,
~ ( ( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> a(X2,X1) ) ) )
& ! [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
=> ! [X4: $i] :
( '$ki_exists_in_world_$i'(X3,X4)
=> ? [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
& b(X5,X4) ) ) ) )
=> ? [X6: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X6)
& ? [X7: $i] :
( '$ki_exists_in_world_$i'(X6,X7)
& ? [X8: '$ki_world'] :
( '$ki_accessible'(X6,X8)
& a(X8,X7)
& b(X8,X7) ) ) ) ),
inference(rectify,[],[f6]) ).
tff(f12,plain,
( ! [X6: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X6)
| ! [X7: $i] :
( ~ '$ki_exists_in_world_$i'(X6,X7)
| ! [X8: '$ki_world'] :
( ~ '$ki_accessible'(X6,X8)
| ~ a(X8,X7)
| ~ b(X8,X7) ) ) )
& ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2: '$ki_world'] :
( a(X2,X1)
| ~ '$ki_accessible'(X0,X2) ) ) )
& ! [X3: '$ki_world'] :
( ! [X4: $i] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
& b(X5,X4) )
| ~ '$ki_exists_in_world_$i'(X3,X4) )
| ~ '$ki_accessible'('$ki_local_world',X3) ) ),
inference(ennf_transformation,[],[f7]) ).
tff(f13,plain,
( ! [X6: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X6)
| ! [X7: $i] :
( ~ '$ki_exists_in_world_$i'(X6,X7)
| ! [X8: '$ki_world'] :
( ~ '$ki_accessible'(X6,X8)
| ~ a(X8,X7)
| ~ b(X8,X7) ) ) )
& ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2: '$ki_world'] :
( a(X2,X1)
| ~ '$ki_accessible'(X0,X2) ) ) )
& ! [X3: '$ki_world'] :
( ! [X4: $i] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
& b(X5,X4) )
| ~ '$ki_exists_in_world_$i'(X3,X4) )
| ~ '$ki_accessible'('$ki_local_world',X3) ) ),
inference(flattening,[],[f12]) ).
tff(f15,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X0,X2)
| ~ a(X2,X1)
| ~ b(X2,X1) ) ) )
& ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ? [X4: $i] :
( '$ki_exists_in_world_$i'(X3,X4)
& ! [X5: '$ki_world'] :
( a(X5,X4)
| ~ '$ki_accessible'(X3,X5) ) ) )
& ! [X6: '$ki_world'] :
( ! [X7: $i] :
( ? [X8: '$ki_world'] :
( '$ki_accessible'(X6,X8)
& b(X8,X7) )
| ~ '$ki_exists_in_world_$i'(X6,X7) )
| ~ '$ki_accessible'('$ki_local_world',X6) ) ),
inference(rectify,[],[f13]) ).
tff(f16,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X0,X2)
| ~ a(X2,X1)
| ~ b(X2,X1) ) ) )
& '$ki_accessible'('$ki_local_world',sK1)
& '$ki_exists_in_world_$i'(sK1,sK2)
& ! [X5: '$ki_world'] :
( a(X5,sK2)
| ~ '$ki_accessible'(sK1,X5) )
& ! [X6: '$ki_world'] :
( ! [X7: $i] :
( ( '$ki_accessible'(X6,sK3(X6,X7))
& b(sK3(X6,X7),X7) )
| ~ '$ki_exists_in_world_$i'(X6,X7) )
| ~ '$ki_accessible'('$ki_local_world',X6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X3,sK1),skolemize(X4,sK2),skolemize(X8,sK3(X6,X7))],[f15]) ).
tff(f21,plain,
! [X6: '$ki_world',X7: $i] :
( b(sK3(X6,X7),X7)
| ~ '$ki_exists_in_world_$i'(X6,X7)
| ~ '$ki_accessible'('$ki_local_world',X6) ),
inference(cnf_transformation,[],[f16]) ).
tff(f22,plain,
! [X6: '$ki_world',X7: $i] :
( '$ki_accessible'(X6,sK3(X6,X7))
| ~ '$ki_exists_in_world_$i'(X6,X7)
| ~ '$ki_accessible'('$ki_local_world',X6) ),
inference(cnf_transformation,[],[f16]) ).
tff(f23,plain,
! [X5: '$ki_world'] :
( a(X5,sK2)
| ~ '$ki_accessible'(sK1,X5) ),
inference(cnf_transformation,[],[f16]) ).
tff(f24,plain,
'$ki_exists_in_world_$i'(sK1,sK2),
inference(cnf_transformation,[],[f16]) ).
tff(f25,plain,
'$ki_accessible'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f16]) ).
tff(f26,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,X2)
| ~ a(X2,X1)
| ~ b(X2,X1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f27,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',sK1)
| ~ '$ki_accessible'(sK1,X0)
| ~ a(X0,sK2)
| ~ b(X0,sK2) ),
inference(resolution,[],[f26,f24]) ).
tff(f28,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK1,X0)
| ~ a(X0,sK2)
| ~ b(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f27,f25]) ).
tff(f29,plain,
! [X0: '$ki_world'] :
( ~ b(X0,sK2)
| ~ '$ki_accessible'(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f28,f23]) ).
tff(f30,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK1,sK3(X0,sK2))
| ~ '$ki_exists_in_world_$i'(X0,sK2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(resolution,[],[f29,f21]) ).
tff(f31,plain,
( ~ '$ki_exists_in_world_$i'(sK1,sK2)
| ~ '$ki_accessible'('$ki_local_world',sK1)
| ~ '$ki_exists_in_world_$i'(sK1,sK2)
| ~ '$ki_accessible'('$ki_local_world',sK1) ),
inference(resolution,[],[f30,f22]) ).
tff(f32,plain,
( ~ '$ki_exists_in_world_$i'(sK1,sK2)
| ~ '$ki_accessible'('$ki_local_world',sK1) ),
inference(duplicate_literal_removal,[],[f31]) ).
tff(f33,plain,
~ '$ki_accessible'('$ki_local_world',sK1),
inference(forward_subsumption_resolution,[],[f32,f24]) ).
tff(f34,plain,
$false,
inference(forward_subsumption_resolution,[],[f33,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO889_16 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.23 % Computer : n011.cluster.edu
% 0.06/0.23 % Model : x86_64 x86_64
% 0.06/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.23 % Memory : 8046.5625MB
% 0.06/0.23 % OS : Linux 6.8.0-71-generic
% 0.06/0.23 % CPULimit : 300
% 0.06/0.23 % WCLimit : 300
% 0.06/0.23 % DateTime : Mon Sep 28 18:40:01 UTC 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.27 Running first-order theorem proving
% 0.16/0.27 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
% 0.17/1.20 % (3629302)Detected formulas, will run a generic FOF schedule.
% 0.17/1.20 % (3629415)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2150182057:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.20 % (3629415)First to succeed.
% 0.17/1.20 % (3629415)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3629302"
% 0.17/1.20 % (3629411)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=4013609388:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.20 % (3629413)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1017953844:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.20 % (3629410)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=3060801565:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.20 % (3629412)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=260640391:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.20 % (3629414)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2453810140:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.20 % (3629414)Also succeeded, but the first one will report.
% 0.17/1.20 % (3629413)Also succeeded, but the first one will report.
% 0.17/1.20 % (3629416)dis-21_1_sil=8000:lcm=predicate:random_seed=3448580625: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)
% 0.17/1.20 % (3629416)Also succeeded, but the first one will report.
% 0.17/1.20 % (3629415)Refutation found. Thanks to Tanya!
% 0.17/1.20 % SZS status Theorem for theBenchmark
% 0.17/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.20 % (3629415)------------------------------
% 0.17/1.20 % (3629415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.20 % (3629415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.20 % (3629415)CaDiCaL version: 2.1.3
% 0.17/1.20 % (3629415)Termination reason: Refutation
% 0.17/1.20 % (3629415)Time elapsed: 0.001 s
% 0.17/1.20 % (3629415)Peak memory usage: 88 MB
% 0.17/1.20 % (3629415)Instructions burned: 2 (million)
% 0.17/1.20 % (3629415)------------------------------
% 0.17/1.20 % (3629415)------------------------------
% 0.17/1.20 % (3629302)Success in time 0.298 s
% 0.17/1.20 % Vampire exiting
%------------------------------------------------------------------------------