%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO888_10 : 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 : n003.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 3.38s 1.15s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 138 ( 49 ~; 36 |; 23 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 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 : 7 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 46 ( 40 !; 6 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_2,type,
sK1: '$ki_world' ).
tff(func_def_3,type,
sK2: '$ki_world' > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
f: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
g: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
h: ( '$ki_world' * $i ) > $o ).
tff(pred_def_5,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f4,conjecture,
( ( ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ( f('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> g(X1,X0) ) ) )
& ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ( g('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> h(X1,X0) ) ) ) )
=> ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ( f('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> h(X1,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f5,negated_conjecture,
~ ( ( ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ( f('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> g(X1,X0) ) ) )
& ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ( g('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> h(X1,X0) ) ) ) )
=> ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ( f('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> h(X1,X0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f6,plain,
~ ( ( ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ( f('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> g(X1,X0) ) ) )
& ! [X2: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X2)
=> ( g('$ki_local_world',X2)
=> ! [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
=> h(X3,X2) ) ) ) )
=> ! [X4: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X4)
=> ( f('$ki_local_world',X4)
=> ! [X5: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X5)
=> h(X5,X4) ) ) ) ),
inference(rectify,[],[f5]) ).
tff(f7,plain,
( ? [X4: $i] :
( ? [X5: '$ki_world'] :
( ~ h(X5,X4)
& '$ki_accessible'('$ki_local_world',X5) )
& f('$ki_local_world',X4)
& '$ki_exists_in_world_$i'('$ki_local_world',X4) )
& ! [X0: $i] :
( ! [X1: '$ki_world'] :
( g(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1) )
| ~ f('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) )
& ! [X2: $i] :
( ! [X3: '$ki_world'] :
( h(X3,X2)
| ~ '$ki_accessible'('$ki_local_world',X3) )
| ~ g('$ki_local_world',X2)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X2) ) ),
inference(ennf_transformation,[],[f6]) ).
tff(f8,plain,
( ? [X4: $i] :
( ? [X5: '$ki_world'] :
( ~ h(X5,X4)
& '$ki_accessible'('$ki_local_world',X5) )
& f('$ki_local_world',X4)
& '$ki_exists_in_world_$i'('$ki_local_world',X4) )
& ! [X0: $i] :
( ! [X1: '$ki_world'] :
( g(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1) )
| ~ f('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) )
& ! [X2: $i] :
( ! [X3: '$ki_world'] :
( h(X3,X2)
| ~ '$ki_accessible'('$ki_local_world',X3) )
| ~ g('$ki_local_world',X2)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X2) ) ),
inference(flattening,[],[f7]) ).
tff(f11,plain,
( ? [X0: $i] :
( ? [X1: '$ki_world'] :
( ~ h(X1,X0)
& '$ki_accessible'('$ki_local_world',X1) )
& f('$ki_local_world',X0)
& '$ki_exists_in_world_$i'('$ki_local_world',X0) )
& ! [X2: $i] :
( ! [X3: '$ki_world'] :
( g(X3,X2)
| ~ '$ki_accessible'('$ki_local_world',X3) )
| ~ f('$ki_local_world',X2)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X2) )
& ! [X4: $i] :
( ! [X5: '$ki_world'] :
( h(X5,X4)
| ~ '$ki_accessible'('$ki_local_world',X5) )
| ~ g('$ki_local_world',X4)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X4) ) ),
inference(rectify,[],[f8]) ).
tff(f12,plain,
( ~ h(sK1,sK0)
& '$ki_accessible'('$ki_local_world',sK1)
& f('$ki_local_world',sK0)
& '$ki_exists_in_world_$i'('$ki_local_world',sK0)
& ! [X2: $i] :
( ! [X3: '$ki_world'] :
( g(X3,X2)
| ~ '$ki_accessible'('$ki_local_world',X3) )
| ~ f('$ki_local_world',X2)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X2) )
& ! [X4: $i] :
( ! [X5: '$ki_world'] :
( h(X5,X4)
| ~ '$ki_accessible'('$ki_local_world',X5) )
| ~ g('$ki_local_world',X4)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11]) ).
tff(f14,plain,
! [X4: $i,X5: '$ki_world'] :
( h(X5,X4)
| ~ '$ki_accessible'('$ki_local_world',X5)
| ~ g('$ki_local_world',X4)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X4) ),
inference(cnf_transformation,[],[f12]) ).
tff(f15,plain,
! [X2: $i,X3: '$ki_world'] :
( g(X3,X2)
| ~ '$ki_accessible'('$ki_local_world',X3)
| ~ f('$ki_local_world',X2)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X2) ),
inference(cnf_transformation,[],[f12]) ).
tff(f16,plain,
'$ki_exists_in_world_$i'('$ki_local_world',sK0),
inference(cnf_transformation,[],[f12]) ).
tff(f17,plain,
f('$ki_local_world',sK0),
inference(cnf_transformation,[],[f12]) ).
tff(f18,plain,
'$ki_accessible'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f12]) ).
tff(f19,plain,
~ h(sK1,sK0),
inference(cnf_transformation,[],[f12]) ).
tff(f21,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f23,plain,
( ~ '$ki_accessible'('$ki_local_world',sK1)
| ~ g('$ki_local_world',sK0)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',sK0) ),
inference(resolution,[],[f14,f19]) ).
tff(f24,plain,
( ~ g('$ki_local_world',sK0)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',sK0) ),
inference(forward_subsumption_resolution,[],[f23,f18]) ).
tff(f25,plain,
~ g('$ki_local_world',sK0),
inference(forward_subsumption_resolution,[],[f24,f16]) ).
tff(f26,plain,
( ~ '$ki_accessible'('$ki_local_world','$ki_local_world')
| ~ f('$ki_local_world',sK0)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',sK0) ),
inference(resolution,[],[f15,f25]) ).
tff(f27,plain,
( ~ '$ki_accessible'('$ki_local_world','$ki_local_world')
| ~ '$ki_exists_in_world_$i'('$ki_local_world',sK0) ),
inference(forward_subsumption_resolution,[],[f26,f17]) ).
tff(f28,plain,
~ '$ki_accessible'('$ki_local_world','$ki_local_world'),
inference(forward_subsumption_resolution,[],[f27,f16]) ).
tff(f29,plain,
$false,
inference(resolution,[],[f21,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO888_10 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n003.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 18:41:43 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.38/1.15 % (1850409)Detected formulas, will run a generic FOF schedule.
% 3.38/1.15 % (1850447)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=3342297265:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.38/1.15 % (1850450)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=215276579:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.38/1.15 % (1850450)First to succeed.
% 3.38/1.15 % (1850450)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1850409"
% 3.38/1.15 % (1850448)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=1419129309:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.38/1.15 % (1850449)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3913362413:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.38/1.15 % (1850446)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=3150556833:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.38/1.15 % (1850449)Also succeeded, but the first one will report.
% 3.38/1.15 % (1850452)dis-21_1_sil=8000:lcm=predicate:random_seed=734530808: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)
% 3.38/1.15 % (1850451)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2235824587:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.38/1.15 % (1850452)Also succeeded, but the first one will report.
% 3.38/1.15 % (1850451)Also succeeded, but the first one will report.
% 3.38/1.15 % (1850450)Refutation found. Thanks to Tanya!
% 3.38/1.15 % SZS status Theorem for theBenchmark
% 3.38/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/1.15 % (1850450)------------------------------
% 3.38/1.15 % (1850450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.15 % (1850450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.15 % (1850450)CaDiCaL version: 2.1.3
% 3.38/1.15 % (1850450)Termination reason: Refutation
% 3.38/1.15 % (1850450)Time elapsed: 0.002 s
% 3.38/1.15 % (1850450)Peak memory usage: 88 MB
% 3.38/1.15 % (1850450)Instructions burned: 1 (million)
% 3.38/1.15 % (1850450)------------------------------
% 3.38/1.15 % (1850450)------------------------------
% 3.38/1.15 % (1850409)Success in time 0.39 s
% 3.38/1.15 % Vampire exiting
%------------------------------------------------------------------------------