%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n004.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 02:32:49 PM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 102 ( 35 ~; 24 |; 13 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 12 ( 12 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 : 36 ( 32 !; 4 ?; 36 :)
% 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' > $i ).
tff(func_def_3,type,
sK2: '$ki_world' ).
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(f9,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(f10,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,[],[f9]) ).
tff(f11,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f14,plain,
'$ki_accessible'('$ki_local_world',sK2),
inference(cnf_transformation,[],[f10]) ).
tff(f15,plain,
~ h(sK2,sK1),
inference(cnf_transformation,[],[f10]) ).
tff(f16,plain,
! [X0: $i,X1: '$ki_world'] :
( g(X1,X0)
| ~ f('$ki_local_world',X0)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f10]) ).
tff(f17,plain,
! [X2: $i,X3: '$ki_world'] :
( h(X3,X2)
| ~ g('$ki_local_world',X2)
| ~ '$ki_accessible'('$ki_local_world',X3)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X2) ),
inference(cnf_transformation,[],[f10]) ).
tff(f18,plain,
'$ki_exists_in_world_$i'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f10]) ).
tff(f19,plain,
f('$ki_local_world',sK1),
inference(cnf_transformation,[],[f10]) ).
tff(f20,plain,
( ~ g('$ki_local_world',sK1)
| ~ '$ki_accessible'('$ki_local_world',sK2)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',sK1) ),
inference(resolution,[],[f17,f15]) ).
tff(f21,plain,
( ~ g('$ki_local_world',sK1)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',sK1) ),
inference(forward_subsumption_resolution,[],[f20,f14]) ).
tff(f22,plain,
~ g('$ki_local_world',sK1),
inference(forward_subsumption_resolution,[],[f21,f18]) ).
tff(f23,plain,
( ~ f('$ki_local_world',sK1)
| ~ '$ki_accessible'('$ki_local_world','$ki_local_world')
| ~ '$ki_exists_in_world_$i'('$ki_local_world',sK1) ),
inference(resolution,[],[f22,f16]) ).
tff(f24,plain,
( ~ '$ki_accessible'('$ki_local_world','$ki_local_world')
| ~ '$ki_exists_in_world_$i'('$ki_local_world',sK1) ),
inference(forward_subsumption_resolution,[],[f23,f19]) ).
tff(f25,plain,
~ '$ki_exists_in_world_$i'('$ki_local_world',sK1),
inference(forward_subsumption_resolution,[],[f24,f11]) ).
tff(f26,plain,
$false,
inference(forward_subsumption_resolution,[],[f25,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO888_10 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n004.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 18:39:52 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
% 0.20/0.26 % (628823)Will run a generic schedule for satisfiability detection.
% 0.20/0.26 % (628832)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2416364050:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.26 % (628832) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-628823-628832"...
% 0.20/0.26 % (628832)...printing done.
% 0.20/0.26 % (628832)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.26 % (628832)------------------------------
% 0.20/0.26 % (628832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (628832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (628832)CaDiCaL version: 2.1.3
% 0.20/0.26 % (628832)Termination reason: Refutation
% 0.20/0.26 % (628832)Time elapsed: 0.001 s
% 0.20/0.26 % (628832)Peak memory usage: 11 MB
% 0.20/0.26 % (628832)Instructions burned: 1 (million)
% 0.20/0.26 % (628823)Success in time 0.023 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------