%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO893_11 : 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 : n015.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 02:32:50 PM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 170 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 205 ( 79 ~; 68 |; 41 &)
% ( 6 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-1 aty)
% Number of variables : 88 ( 0 sgn 59 !; 29 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_1,type,
sK1: '$ki_world' > '$ki_world' ).
tff(func_def_2,type,
sK2: '$ki_world' ).
tff(func_def_3,type,
sK3: '$ki_world' > '$ki_world' ).
tff(func_def_4,type,
sK4: '$ki_world' > '$ki_world' ).
tff(func_def_5,type,
sK5: '$ki_world' ).
tff(func_def_6,type,
sK6: '$ki_world' > '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
p: '$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'('$ki_local_world',X0)
=> ? [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X1,X2)
=> p(X2) ) ) )
<=> ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> ? [X2: '$ki_world'] :
( '$ki_accessible'(X1,X2)
& ~ p(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f3,negated_conjecture,
~ ( ~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X1,X2)
=> p(X2) ) ) )
<=> ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> ? [X2: '$ki_world'] :
( '$ki_accessible'(X1,X2)
& ~ p(X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
~ ( ~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X1,X2)
=> p(X2) ) ) )
<=> ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( '$ki_accessible'(X3,X4)
=> ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f5,plain,
( ? [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) )
& '$ki_accessible'('$ki_local_world',X0) )
<~> ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(X3,X4) ) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,definition,
( sP0
<=> ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(X3,X4) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f7,plain,
( ? [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) )
& '$ki_accessible'('$ki_local_world',X0) )
<~> sP0 ),
inference(definition_folding,[],[f5,f6]) ).
tff(f8,plain,
( ( sP0
| ! [X3: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X3)
| ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| p(X5) )
& '$ki_accessible'(X3,X4) ) ) )
& ( ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(X3,X4) ) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f9,plain,
( ( sP0
| ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ? [X1: '$ki_world'] :
( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X1,X2)
| p(X2) )
& '$ki_accessible'(X0,X1) ) ) )
& ( ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(X3,X4) ) )
| ~ sP0 ) ),
inference(rectify,[],[f8]) ).
tff(f10,plain,
( ( sP0
| ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(sK1(X0),X2)
| p(X2) )
& '$ki_accessible'(X0,sK1(X0)) ) ) )
& ( ( '$ki_accessible'('$ki_local_world',sK2)
& ! [X4: '$ki_world'] :
( ( '$ki_accessible'(X4,sK3(X4))
& ~ p(sK3(X4)) )
| ~ '$ki_accessible'(sK2,X4) ) )
| ~ sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X1,sK1(X0)),skolemize(X3,sK2),skolemize(X5,sK3(X4))],[f9]) ).
tff(f11,plain,
( ( ~ sP0
| ! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
& ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) )
& ( sP0
| ? [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) )
& '$ki_accessible'('$ki_local_world',X0) ) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f12,plain,
( ( ~ sP0
| ! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
& ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) )
& ( sP0
| ? [X3: '$ki_world'] :
( ! [X4: '$ki_world'] :
( ~ '$ki_accessible'(X3,X4)
| ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) ) )
& '$ki_accessible'('$ki_local_world',X3) ) ) ),
inference(rectify,[],[f11]) ).
tff(f13,plain,
( ( ~ sP0
| ! [X0: '$ki_world'] :
( ( '$ki_accessible'(X0,sK4(X0))
& ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(sK4(X0),X2) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) )
& ( sP0
| ( ! [X4: '$ki_world'] :
( ~ '$ki_accessible'(sK5,X4)
| ( ~ p(sK6(X4))
& '$ki_accessible'(X4,sK6(X4)) ) )
& '$ki_accessible'('$ki_local_world',sK5) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X1,sK4(X0)),skolemize(X3,sK5),skolemize(X5,sK6(X4))],[f12]) ).
tff(f14,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f1]) ).
tff(f15,plain,
! [X4: '$ki_world'] :
( ~ p(sK3(X4))
| ~ '$ki_accessible'(sK2,X4)
| ~ sP0 ),
inference(cnf_transformation,[],[f10]) ).
tff(f19,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( sP0
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(sK1(X0),X2)
| p(X2) ),
inference(cnf_transformation,[],[f10]) ).
tff(f22,plain,
! [X4: '$ki_world'] :
( sP0
| ~ '$ki_accessible'(sK5,X4)
| ~ p(sK6(X4)) ),
inference(cnf_transformation,[],[f13]) ).
tff(f23,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ sP0
| p(X2)
| ~ '$ki_accessible'(sK4(X0),X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f13]) ).
tff(f26,definition,
( spl7_1
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
tff(f28,plain,
( ~ sP0
| spl7_1 ),
inference(avatar_component_clause,[],[f26]) ).
tff(f36,definition,
( spl7_4
<=> ! [X4: '$ki_world'] :
( ~ p(sK3(X4))
| ~ '$ki_accessible'(sK2,X4) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
tff(f37,plain,
( ! [X4: '$ki_world'] :
( ~ p(sK3(X4))
| ~ '$ki_accessible'(sK2,X4) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f36]) ).
tff(f38,plain,
( ~ spl7_1
| spl7_4 ),
inference(avatar_split_clause,[],[f15,f36,f26]) ).
tff(f40,plain,
( ! [X4: '$ki_world'] :
( ~ p(sK6(X4))
| ~ '$ki_accessible'(sK5,X4) )
| spl7_1 ),
inference(forward_subsumption_resolution,[],[f22,f28]) ).
tff(f51,plain,
( ! [X2: '$ki_world',X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(sK1(X0),X2)
| p(X2) )
| spl7_1 ),
inference(forward_subsumption_resolution,[],[f19,f28]) ).
tff(f52,plain,
( ! [X2: '$ki_world',X0: '$ki_world'] :
( ~ '$ki_accessible'(sK1(X0),X2)
| p(X2) )
| spl7_1 ),
inference(forward_subsumption_resolution,[],[f51,f14]) ).
tff(f53,plain,
( ! [X2: '$ki_world'] : p(X2)
| spl7_1 ),
inference(forward_subsumption_resolution,[],[f52,f14]) ).
tff(f56,plain,
( ! [X0: '$ki_world'] : ~ '$ki_accessible'(sK5,X0)
| spl7_1 ),
inference(resolution,[],[f53,f40]) ).
tff(f59,plain,
( $false
| spl7_1 ),
inference(forward_subsumption_resolution,[],[f56,f14]) ).
tff(f60,plain,
spl7_1,
inference(avatar_contradiction_clause,[],[f59]) ).
tff(f61,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ sP0
| p(X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f23,f14]) ).
tff(f62,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( sP0
| ~ '$ki_accessible'(sK1(X0),X2)
| p(X2) ),
inference(forward_subsumption_resolution,[],[f19,f14]) ).
tff(f63,plain,
! [X2: '$ki_world'] :
( ~ sP0
| p(X2) ),
inference(forward_subsumption_resolution,[],[f61,f14]) ).
tff(f64,plain,
! [X2: '$ki_world'] :
( sP0
| p(X2) ),
inference(forward_subsumption_resolution,[],[f62,f14]) ).
tff(f65,plain,
! [X2: '$ki_world'] : p(X2),
inference(global_subsumption,[],[f64,f63]) ).
tff(f66,plain,
! [X2: '$ki_world'] : p(X2),
inference(global_subsumption,[],[f65]) ).
tff(f72,plain,
( ! [X4: '$ki_world'] : ~ '$ki_accessible'(sK2,X4)
| ~ spl7_4 ),
inference(forward_subsumption_resolution,[],[f37,f66]) ).
tff(f74,plain,
( $false
| ~ spl7_4 ),
inference(forward_subsumption_resolution,[],[f72,f14]) ).
tff(f75,plain,
~ spl7_4,
inference(avatar_contradiction_clause,[],[f74]) ).
cnf(s13,plain,
( ~ spl7_1
| spl7_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s35,plain,
spl7_1,
inference(sat_conversion,[],[f60]) ).
cnf(s45,plain,
~ spl7_4,
inference(sat_conversion,[],[f75]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s13,s45,s35]) ).
tff(f76,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO893_11 : 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 : n015.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 18:43:17 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
% 0.09/0.24 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
% 0.22/0.28 % (2879433)Will run a generic schedule for satisfiability detection.
% 0.22/0.28 % (2879440)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=304160020:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.28 % (2879440) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2879433-2879440"...
% 0.22/0.28 % (2879440)...printing done.
% 0.22/0.28 % (2879439)% WARNING: option uhcvi not known.
% 0.22/0.28 % (2879440)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (2879440)------------------------------
% 0.22/0.28 % (2879440)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (2879440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (2879440)CaDiCaL version: 2.1.3
% 0.22/0.28 % (2879440)Termination reason: Refutation
% 0.22/0.28 % (2879440)Time elapsed: 0.002 s
% 0.22/0.28 % (2879440)Peak memory usage: 12 MB
% 0.22/0.28 % (2879440)Instructions burned: 2 (million)
% 0.22/0.28 % (2879433)Success in time 0.032 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------