%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO896_7 : 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 : n020.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 0.18s 1.21s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 90 ( 36 ~; 21 |; 18 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 23 ( 17 !; 6 ?; 23 :)
% 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(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
p: '$ki_world' > $o ).
tff(pred_def_3,type,
q: '$ki_world' > $o ).
tff(f1,conjecture,
( ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
=> q(X0) ) )
& ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
=> ~ q(X0) ) ) )
=> ~ ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& p(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f2,negated_conjecture,
~ ( ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
=> q(X0) ) )
& ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
=> ~ q(X0) ) ) )
=> ~ ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& p(X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
=> q(X0) ) )
& ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( p(X1)
=> ~ q(X1) ) ) )
=> ~ ? [X2: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X2)
& p(X2) ) ),
inference(rectify,[],[f2]) ).
tff(f4,plain,
( ? [X2: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X2)
& p(X2) )
& ! [X0: '$ki_world'] :
( q(X0)
| ~ p(X0)
| ~ '$ki_accessible'('$ki_local_world',X0) )
& ! [X1: '$ki_world'] :
( ~ q(X1)
| ~ p(X1)
| ~ '$ki_accessible'('$ki_local_world',X1) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
( ? [X2: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X2)
& p(X2) )
& ! [X0: '$ki_world'] :
( q(X0)
| ~ p(X0)
| ~ '$ki_accessible'('$ki_local_world',X0) )
& ! [X1: '$ki_world'] :
( ~ q(X1)
| ~ p(X1)
| ~ '$ki_accessible'('$ki_local_world',X1) ) ),
inference(flattening,[],[f4]) ).
tff(f6,plain,
( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& p(X0) )
& ! [X1: '$ki_world'] :
( q(X1)
| ~ p(X1)
| ~ '$ki_accessible'('$ki_local_world',X1) )
& ! [X2: '$ki_world'] :
( ~ q(X2)
| ~ p(X2)
| ~ '$ki_accessible'('$ki_local_world',X2) ) ),
inference(rectify,[],[f5]) ).
tff(f7,plain,
( '$ki_accessible'('$ki_local_world',sK0)
& p(sK0)
& ! [X1: '$ki_world'] :
( q(X1)
| ~ p(X1)
| ~ '$ki_accessible'('$ki_local_world',X1) )
& ! [X2: '$ki_world'] :
( ~ q(X2)
| ~ p(X2)
| ~ '$ki_accessible'('$ki_local_world',X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
tff(f8,plain,
! [X2: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ p(X2)
| ~ q(X2) ),
inference(cnf_transformation,[],[f7]) ).
tff(f9,plain,
! [X1: '$ki_world'] :
( q(X1)
| ~ p(X1)
| ~ '$ki_accessible'('$ki_local_world',X1) ),
inference(cnf_transformation,[],[f7]) ).
tff(f10,plain,
p(sK0),
inference(cnf_transformation,[],[f7]) ).
tff(f11,plain,
'$ki_accessible'('$ki_local_world',sK0),
inference(cnf_transformation,[],[f7]) ).
tff(f14,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ p(X1) ),
inference(forward_subsumption_resolution,[],[f9,f8]) ).
tff(f15,plain,
~ p(sK0),
inference(resolution,[],[f14,f11]) ).
tff(f16,plain,
$false,
inference(forward_subsumption_resolution,[],[f15,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO896_7 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n020.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 18:41:19 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 0.18/1.21 % (406806)Detected formulas, will run a generic FOF schedule.
% 0.18/1.21 % (406902)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=987781805:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/1.21 % (406902)First to succeed.
% 0.18/1.21 % (406902)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-406806"
% 0.18/1.21 % (406894)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=1183449081:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/1.21 % (406900)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1423732241:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/1.21 % (406897)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=808067638:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/1.21 % (406900)Also succeeded, but the first one will report.
% 0.18/1.21 % (406906)dis-21_1_sil=8000:lcm=predicate:random_seed=4011547474: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)
% 0.18/1.21 % (406904)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=214857666:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/1.21 % (406904)Also succeeded, but the first one will report.
% 0.18/1.21 % (406906)Also succeeded, but the first one will report.
% 0.18/1.21 % (406898)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=1987542189:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/1.21 % (406902)Refutation found. Thanks to Tanya!
% 0.18/1.21 % SZS status Theorem for theBenchmark
% 0.18/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.21 % (406902)------------------------------
% 0.18/1.21 % (406902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.21 % (406902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.21 % (406902)CaDiCaL version: 2.1.3
% 0.18/1.21 % (406902)Termination reason: Refutation
% 0.18/1.21 % (406902)Time elapsed: 0.001 s
% 0.18/1.21 % (406902)Peak memory usage: 88 MB
% 0.18/1.21 % (406902)------------------------------
% 0.18/1.21 % (406902)------------------------------
% 0.18/1.21 % (406806)Success in time 0.308 s
% 0.18/1.21 % Vampire exiting
%------------------------------------------------------------------------------