%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO901_11 : 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 : n019.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 02:29:19 PM UTC 2026
% Result : Theorem 3.68s 1.51s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 152 ( 52 ~; 51 |; 26 &)
% ( 7 <=>; 15 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 53 ( 43 !; 10 ?; 53 :)
% 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: '$ki_world' ).
tff(func_def_3,type,
sK2: '$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' > $o ).
tff(f1,axiom,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
tff(f2,conjecture,
( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
<=> q(X0) ) )
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> p(X1) )
<=> ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> q(X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f3,negated_conjecture,
~ ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
<=> q(X0) ) )
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> p(X1) )
<=> ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> q(X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
~ ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
<=> q(X0) ) )
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( ! [X2: '$ki_world'] :
( '$ki_accessible'(X1,X2)
=> p(X2) )
<=> ! [X3: '$ki_world'] :
( '$ki_accessible'(X1,X3)
=> q(X3) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f5,plain,
( ? [X1: '$ki_world'] :
( ( ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) )
<~> ! [X3: '$ki_world'] :
( q(X3)
| ~ '$ki_accessible'(X1,X3) ) )
& '$ki_accessible'('$ki_local_world',X1) )
& ! [X0: '$ki_world'] :
( ( p(X0)
<=> q(X0) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
( ? [X1: '$ki_world'] :
( ( ? [X3: '$ki_world'] :
( ~ q(X3)
& '$ki_accessible'(X1,X3) )
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) )
& ( ! [X3: '$ki_world'] :
( q(X3)
| ~ '$ki_accessible'(X1,X3) )
| ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) ) )
& '$ki_accessible'('$ki_local_world',X1) )
& ! [X0: '$ki_world'] :
( ( ( p(X0)
| ~ q(X0) )
& ( q(X0)
| ~ p(X0) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f7,plain,
( ? [X1: '$ki_world'] :
( ( ? [X3: '$ki_world'] :
( ~ q(X3)
& '$ki_accessible'(X1,X3) )
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) )
& ( ! [X3: '$ki_world'] :
( q(X3)
| ~ '$ki_accessible'(X1,X3) )
| ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) ) )
& '$ki_accessible'('$ki_local_world',X1) )
& ! [X0: '$ki_world'] :
( ( ( p(X0)
| ~ q(X0) )
& ( q(X0)
| ~ p(X0) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) ),
inference(flattening,[],[f6]) ).
tff(f8,plain,
( ? [X0: '$ki_world'] :
( ( ? [X1: '$ki_world'] :
( ~ q(X1)
& '$ki_accessible'(X0,X1) )
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X0,X2) ) )
& ( ! [X3: '$ki_world'] :
( q(X3)
| ~ '$ki_accessible'(X0,X3) )
| ! [X4: '$ki_world'] :
( p(X4)
| ~ '$ki_accessible'(X0,X4) ) )
& '$ki_accessible'('$ki_local_world',X0) )
& ! [X5: '$ki_world'] :
( ( ( p(X5)
| ~ q(X5) )
& ( q(X5)
| ~ p(X5) ) )
| ~ '$ki_accessible'('$ki_local_world',X5) ) ),
inference(rectify,[],[f7]) ).
tff(f9,plain,
( ( ( ~ q(sK1)
& '$ki_accessible'(sK0,sK1) )
| ( ~ p(sK2)
& '$ki_accessible'(sK0,sK2) ) )
& ( ! [X3: '$ki_world'] :
( q(X3)
| ~ '$ki_accessible'(sK0,X3) )
| ! [X4: '$ki_world'] :
( p(X4)
| ~ '$ki_accessible'(sK0,X4) ) )
& '$ki_accessible'('$ki_local_world',sK0)
& ! [X5: '$ki_world'] :
( ( ( p(X5)
| ~ q(X5) )
& ( q(X5)
| ~ p(X5) ) )
| ~ '$ki_accessible'('$ki_local_world',X5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
tff(f10,plain,
! [X5: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X5)
| ~ p(X5)
| q(X5) ),
inference(cnf_transformation,[],[f9]) ).
tff(f11,plain,
! [X5: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X5)
| ~ q(X5)
| p(X5) ),
inference(cnf_transformation,[],[f9]) ).
tff(f13,plain,
! [X3: '$ki_world',X4: '$ki_world'] :
( ~ '$ki_accessible'(sK0,X4)
| ~ '$ki_accessible'(sK0,X3)
| p(X4)
| q(X3) ),
inference(cnf_transformation,[],[f9]) ).
tff(f15,plain,
( '$ki_accessible'(sK0,sK1)
| ~ p(sK2) ),
inference(cnf_transformation,[],[f9]) ).
tff(f17,plain,
( ~ q(sK1)
| ~ p(sK2) ),
inference(cnf_transformation,[],[f9]) ).
tff(f18,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f1]) ).
tff(f24,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK0,X0)
| p(X0)
| q(X0) ),
inference(factoring,[],[f13]) ).
tff(f27,plain,
( p(sK1)
| q(sK1)
| ~ p(sK2) ),
inference(resolution,[],[f24,f15]) ).
tff(f32,plain,
( p(sK1)
| ~ p(sK2) ),
inference(forward_subsumption_resolution,[],[f27,f17]) ).
tff(f33,plain,
! [X0: '$ki_world'] :
( p(X0)
| ~ q(X0) ),
inference(resolution,[],[f18,f11]) ).
tff(f34,plain,
! [X0: '$ki_world'] :
( q(X0)
| ~ p(X0) ),
inference(resolution,[],[f18,f10]) ).
tff(f36,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(sK0,X0)
| p(X1)
| q(X0) ),
inference(resolution,[],[f18,f13]) ).
tff(f37,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( q(X0)
| p(X1) ),
inference(forward_subsumption_resolution,[],[f36,f18]) ).
tff(f38,plain,
( ~ p(sK1)
| ~ p(sK2) ),
inference(resolution,[],[f34,f17]) ).
tff(f42,plain,
~ p(sK2),
inference(forward_subsumption_resolution,[],[f38,f32]) ).
tff(f43,plain,
~ q(sK2),
inference(resolution,[],[f42,f33]) ).
tff(f46,plain,
! [X0: '$ki_world'] : p(X0),
inference(resolution,[],[f43,f37]) ).
tff(f51,plain,
$false,
inference(resolution,[],[f46,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO901_11 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 % Computer : n019.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Mon Sep 28 18:40:48 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.28 Running first-order theorem proving
% 0.25/0.28 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
% 3.68/1.51 % (82646)Detected formulas, will run a generic FOF schedule.
% 3.68/1.51 % (82661)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3760559748:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.68/1.51 % (82661)First to succeed.
% 3.68/1.51 % (82661)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-82646"
% 3.68/1.51 % (82663)dis-21_1_sil=8000:lcm=predicate:random_seed=1442354515: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)
% 3.68/1.51 % (82663)Also succeeded, but the first one will report.
% 3.68/1.51 % (82660)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1285178839:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.68/1.51 % (82658)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=2158794530:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.68/1.51 % (82657)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=2818254785:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.68/1.51 % (82660)Also succeeded, but the first one will report.
% 3.68/1.51 % (82662)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1974858049:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.68/1.51 % (82659)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=1178684973:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.68/1.51 % (82662)Also succeeded, but the first one will report.
% 3.68/1.51 % (82661)Refutation found. Thanks to Tanya!
% 3.68/1.51 % SZS status Theorem for theBenchmark
% 3.68/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.51 % (82661)------------------------------
% 3.68/1.51 % (82661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.51 % (82661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.51 % (82661)CaDiCaL version: 2.1.3
% 3.68/1.51 % (82661)Termination reason: Refutation
% 3.68/1.51 % (82661)Time elapsed: 0.002 s
% 3.68/1.51 % (82661)Peak memory usage: 88 MB
% 3.68/1.51 % (82661)Instructions burned: 1 (million)
% 3.68/1.51 % (82661)------------------------------
% 3.68/1.51 % (82661)------------------------------
% 3.68/1.51 % (82646)Success in time 0.396 s
% 3.68/1.51 % Vampire exiting
%------------------------------------------------------------------------------