%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO887_22 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 02:32:48 PM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 65 ( 27 ~; 17 |; 15 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 3 ( 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 : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 31 ( 20 !; 11 ?; 31 :)
% 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' > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
f: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f5,conjecture,
( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& f(X0,X1) ) )
=> ? [X1: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X1)
& ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& f(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f6,negated_conjecture,
~ ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& f(X0,X1) ) )
=> ? [X1: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X1)
& ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& f(X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f7,plain,
~ ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& f(X0,X1) ) )
=> ? [X2: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X2)
& ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& f(X3,X2) ) ) ),
inference(rectify,[],[f6]) ).
tff(f12,plain,
( ! [X2: $i] :
( ~ '$ki_exists_in_world_$i'('$ki_local_world',X2)
| ! [X3: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X3)
| ~ f(X3,X2) ) )
& ! [X0: '$ki_world'] :
( ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& f(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) ),
inference(ennf_transformation,[],[f7]) ).
tff(f14,plain,
( ! [X0: $i] :
( ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
| ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ f(X1,X0) ) )
& ! [X2: '$ki_world'] :
( ? [X3: $i] :
( '$ki_exists_in_world_$i'(X2,X3)
& f(X2,X3) )
| ~ '$ki_accessible'('$ki_local_world',X2) ) ),
inference(rectify,[],[f12]) ).
tff(f15,plain,
( ! [X0: $i] :
( ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
| ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ f(X1,X0) ) )
& ! [X2: '$ki_world'] :
( ( '$ki_exists_in_world_$i'(X2,sK1(X2))
& f(X2,sK1(X2)) )
| ~ '$ki_accessible'('$ki_local_world',X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X2))],[f14]) ).
tff(f16,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f20,plain,
! [X2: '$ki_world'] :
( f(X2,sK1(X2))
| ~ '$ki_accessible'('$ki_local_world',X2) ),
inference(cnf_transformation,[],[f15]) ).
tff(f21,plain,
! [X2: '$ki_world'] :
( '$ki_exists_in_world_$i'(X2,sK1(X2))
| ~ '$ki_accessible'('$ki_local_world',X2) ),
inference(cnf_transformation,[],[f15]) ).
tff(f22,plain,
! [X0: $i,X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ f(X1,X0) ),
inference(cnf_transformation,[],[f15]) ).
tff(f43,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world','$ki_local_world')
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ f(X0,sK1('$ki_local_world')) ),
inference(resolution,[],[f21,f22]) ).
tff(f44,plain,
! [X0: '$ki_world'] :
( ~ f(X0,sK1('$ki_local_world'))
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f43,f16]) ).
tff(f51,plain,
( ~ '$ki_accessible'('$ki_local_world','$ki_local_world')
| ~ '$ki_accessible'('$ki_local_world','$ki_local_world') ),
inference(resolution,[],[f44,f20]) ).
tff(f52,plain,
~ '$ki_accessible'('$ki_local_world','$ki_local_world'),
inference(duplicate_literal_removal,[],[f51]) ).
tff(f53,plain,
$false,
inference(forward_subsumption_resolution,[],[f52,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO887_22 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n006.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 18:39:40 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.26 % (32490)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (32497)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=820004439:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.09/0.26 % (32497) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-32490-32497"...
% 0.09/0.26 % (32497)...printing done.
% 0.09/0.26 % (32497)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (32497)------------------------------
% 0.09/0.26 % (32497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (32497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (32497)CaDiCaL version: 2.1.3
% 0.09/0.26 % (32497)Termination reason: Refutation
% 0.09/0.26 % (32497)Time elapsed: 0.001 s
% 0.09/0.26 % (32497)Peak memory usage: 11 MB
% 0.09/0.26 % (32497)Instructions burned: 1 (million)
% 0.09/0.26 % (32490)Success in time 0.015 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------