%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PLA054_4 : 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 : n026.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 12:28:32 PM UTC 2026
% Result : Theorem 2.70s 1.28s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 13 unt; 0 typ; 5 def)
% Number of atoms : 355 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 428 ( 175 ~; 176 |; 40 &)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 30 ( 30 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 13 usr; 8 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 143 ( 0 sgn 129 !; 14 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_4,type,
sK0: '$ki_world' > $i ).
tff(func_def_5,type,
sK1: ( '$ki_world' * $i * $i ) > $i ).
tff(func_def_7,type,
sK3: '$ki_world' ).
tff(func_def_8,type,
sK4: '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
h: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
closed: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
combo: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_5,type,
open: ( '$ki_world' * $i ) > $o ).
tff(pred_def_6,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f2,axiom,
! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
( ( '$ki_accessible'(X0,X1)
& '$ki_accessible'(X1,X2) )
=> '$ki_accessible'(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
tff(f3,axiom,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f5,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: $i] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ? [X3: $i] :
( '$ki_exists_in_world_$i'(X0,X3)
& ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ( ( closed(X4,X1)
& combo(X4,X1,X2)
& h(X4,X3) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> open(X5,X1) ) ) )
& ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ( ( closed(X4,X1)
& ~ combo(X4,X1,X2)
& h(X4,o) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> closed(X5,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f6,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> closed(X0,d) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f10,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ? [X2: $i] :
( '$ki_exists_in_world_$i'(X0,X2)
& ( ! [X3: '$ki_world'] :
( '$ki_accessible'(X0,X3)
=> ( combo(X3,d,X1)
& h(X3,X2) ) )
=> ! [X3: '$ki_world'] :
( '$ki_accessible'(X0,X3)
=> open(X3,d) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f11,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ? [X2: $i] :
( '$ki_exists_in_world_$i'(X0,X2)
& ( ! [X3: '$ki_world'] :
( '$ki_accessible'(X0,X3)
=> ( combo(X3,d,X1)
& h(X3,X2) ) )
=> ! [X3: '$ki_world'] :
( '$ki_accessible'(X0,X3)
=> open(X3,d) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
tff(f12,plain,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ! [X2: $i] :
( '$ki_exists_in_world_$i'(X0,X2)
=> ? [X3: $i] :
( '$ki_exists_in_world_$i'(X0,X3)
& ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> ( ( closed(X4,X1)
& combo(X4,X1,X2)
& h(X4,X3) )
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> open(X5,X1) ) ) )
& ! [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
=> ( ( closed(X6,X1)
& ~ combo(X6,X1,X2)
& h(X6,o) )
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X6,X7)
=> closed(X7,X1) ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
tff(f13,plain,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ? [X2: $i] :
( '$ki_exists_in_world_$i'(X0,X2)
& ( ! [X3: '$ki_world'] :
( '$ki_accessible'(X0,X3)
=> ( combo(X3,d,X1)
& h(X3,X2) ) )
=> ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> open(X4,d) ) ) ) ) ),
inference(rectify,[],[f11]) ).
tff(f14,plain,
! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
tff(f15,plain,
! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(X1,X2) ),
inference(flattening,[],[f14]) ).
tff(f16,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: $i] :
( ? [X3: $i] :
( '$ki_exists_in_world_$i'(X0,X3)
& ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( open(X5,X1)
| ~ '$ki_accessible'(X4,X5) )
| ~ closed(X4,X1)
| ~ combo(X4,X1,X2)
| ~ h(X4,X3)
| ~ '$ki_accessible'(X0,X4) )
& ! [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( closed(X7,X1)
| ~ '$ki_accessible'(X6,X7) )
| ~ closed(X6,X1)
| combo(X6,X1,X2)
| ~ h(X6,o)
| ~ '$ki_accessible'(X0,X6) ) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f12]) ).
tff(f17,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: $i] :
( ? [X3: $i] :
( '$ki_exists_in_world_$i'(X0,X3)
& ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( open(X5,X1)
| ~ '$ki_accessible'(X4,X5) )
| ~ closed(X4,X1)
| ~ combo(X4,X1,X2)
| ~ h(X4,X3)
| ~ '$ki_accessible'(X0,X4) )
& ! [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( closed(X7,X1)
| ~ '$ki_accessible'(X6,X7) )
| ~ closed(X6,X1)
| combo(X6,X1,X2)
| ~ h(X6,o)
| ~ '$ki_accessible'(X0,X6) ) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f16]) ).
tff(f18,plain,
! [X0: '$ki_world'] :
( closed(X0,d)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f6]) ).
tff(f24,plain,
? [X0: '$ki_world'] :
( ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| ( ? [X4: '$ki_world'] :
( ~ open(X4,d)
& '$ki_accessible'(X0,X4) )
& ! [X3: '$ki_world'] :
( ( combo(X3,d,X1)
& h(X3,X2) )
| ~ '$ki_accessible'(X0,X3) ) ) ) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f13]) ).
tff(f26,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: $i] :
( ( '$ki_exists_in_world_$i'(X0,sK1(X0,X1,X2))
& ! [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( open(X5,X1)
| ~ '$ki_accessible'(X4,X5) )
| ~ closed(X4,X1)
| ~ combo(X4,X1,X2)
| ~ h(X4,sK1(X0,X1,X2))
| ~ '$ki_accessible'(X0,X4) )
& ! [X6: '$ki_world'] :
( ! [X7: '$ki_world'] :
( closed(X7,X1)
| ~ '$ki_accessible'(X6,X7) )
| ~ closed(X6,X1)
| combo(X6,X1,X2)
| ~ h(X6,o)
| ~ '$ki_accessible'(X0,X6) ) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f17]) ).
tff(f28,plain,
? [X0: '$ki_world'] :
( ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| ( ? [X3: '$ki_world'] :
( ~ open(X3,d)
& '$ki_accessible'(X0,X3) )
& ! [X4: '$ki_world'] :
( ( combo(X4,d,X1)
& h(X4,X2) )
| ~ '$ki_accessible'(X0,X4) ) ) ) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(rectify,[],[f24]) ).
tff(f29,plain,
( ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(sK3,X1)
| ! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK3,X2)
| ( ~ open(sK4,d)
& '$ki_accessible'(sK3,sK4)
& ! [X4: '$ki_world'] :
( ( combo(X4,d,X1)
& h(X4,X2) )
| ~ '$ki_accessible'(sK3,X4) ) ) ) )
& '$ki_accessible'('$ki_local_world',sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X3,sK4)],[f28]) ).
tff(f30,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f31,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
( '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tff(f32,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f3]) ).
tff(f35,plain,
! [X2: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( open(X5,X1)
| ~ '$ki_accessible'(X4,X5)
| ~ closed(X4,X1)
| ~ combo(X4,X1,X2)
| ~ h(X4,sK1(X0,X1,X2))
| ~ '$ki_accessible'(X0,X4)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f26]) ).
tff(f37,plain,
! [X0: '$ki_world'] :
( closed(X0,d)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f18]) ).
tff(f42,plain,
'$ki_accessible'('$ki_local_world',sK3),
inference(cnf_transformation,[],[f29]) ).
tff(f43,plain,
! [X2: $i,X1: $i,X4: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(sK3,X1)
| ~ '$ki_exists_in_world_$i'(sK3,X2)
| h(X4,X2)
| ~ '$ki_accessible'(sK3,X4) ),
inference(cnf_transformation,[],[f29]) ).
tff(f44,plain,
! [X2: $i,X1: $i,X4: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(sK3,X1)
| ~ '$ki_exists_in_world_$i'(sK3,X2)
| combo(X4,d,X1)
| ~ '$ki_accessible'(sK3,X4) ),
inference(cnf_transformation,[],[f29]) ).
tff(f45,plain,
! [X2: $i,X1: $i] :
( ~ '$ki_exists_in_world_$i'(sK3,X1)
| ~ '$ki_exists_in_world_$i'(sK3,X2)
| '$ki_accessible'(sK3,sK4) ),
inference(cnf_transformation,[],[f29]) ).
tff(f46,plain,
! [X2: $i,X1: $i] :
( ~ '$ki_exists_in_world_$i'(sK3,X1)
| ~ '$ki_exists_in_world_$i'(sK3,X2)
| ~ open(sK4,d) ),
inference(cnf_transformation,[],[f29]) ).
tff(f48,definition,
( spl5_1
<=> ! [X2: $i,X4: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(sK3,X2)
| ~ '$ki_accessible'(sK3,X4)
| h(X4,X2) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f49,plain,
( ! [X2: $i,X4: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(sK3,X2)
| ~ '$ki_accessible'(sK3,X4)
| h(X4,X2) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f48]) ).
tff(f51,definition,
( spl5_2
<=> ! [X1: $i] : ~ '$ki_exists_in_world_$i'(sK3,X1) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f52,plain,
( ! [X1: $i] : ~ '$ki_exists_in_world_$i'(sK3,X1)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f51]) ).
tff(f53,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f43,f51,f48]) ).
tff(f55,definition,
( spl5_3
<=> ! [X4: '$ki_world',X1: $i] :
( ~ '$ki_exists_in_world_$i'(sK3,X1)
| ~ '$ki_accessible'(sK3,X4)
| combo(X4,d,X1) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
tff(f56,plain,
( ! [X1: $i,X4: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(sK3,X1)
| ~ '$ki_accessible'(sK3,X4)
| combo(X4,d,X1) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f55]) ).
tff(f57,plain,
( spl5_2
| spl5_3 ),
inference(avatar_split_clause,[],[f44,f55,f51]) ).
tff(f59,definition,
( spl5_4
<=> '$ki_accessible'(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
tff(f61,plain,
( '$ki_accessible'(sK3,sK4)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f59]) ).
tff(f62,plain,
( spl5_4
| spl5_2
| spl5_2 ),
inference(avatar_split_clause,[],[f45,f51,f51,f59]) ).
tff(f64,definition,
( spl5_5
<=> open(sK4,d) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
tff(f66,plain,
( ~ open(sK4,d)
| spl5_5 ),
inference(avatar_component_clause,[],[f64]) ).
tff(f67,plain,
( ~ spl5_5
| spl5_2
| spl5_2 ),
inference(avatar_split_clause,[],[f46,f51,f51,f64]) ).
tff(f68,plain,
( $false
| ~ spl5_2 ),
inference(resolution,[],[f32,f52]) ).
tff(f69,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f68]) ).
tff(f70,plain,
( ! [X2: $i,X4: '$ki_world'] :
( h(X4,X2)
| ~ '$ki_accessible'(sK3,X4) )
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f49,f32]) ).
tff(f71,plain,
( ! [X1: $i,X4: '$ki_world'] :
( combo(X4,d,X1)
| ~ '$ki_accessible'(sK3,X4) )
| ~ spl5_3 ),
inference(forward_subsumption_resolution,[],[f56,f32]) ).
tff(f75,plain,
! [X2: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( open(X5,X1)
| ~ '$ki_accessible'(X4,X5)
| ~ closed(X4,X1)
| ~ combo(X4,X1,X2)
| ~ h(X4,sK1(X0,X1,X2))
| ~ '$ki_accessible'(X0,X4)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f35,f32]) ).
tff(f76,plain,
! [X2: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
( ~ h(X4,sK1(X0,X1,X2))
| ~ '$ki_accessible'(X4,X5)
| ~ closed(X4,X1)
| ~ combo(X4,X1,X2)
| open(X5,X1)
| ~ '$ki_accessible'(X0,X4)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f75,f32]) ).
tff(f77,plain,
( ! [X2: $i,X3: $i,X0: '$ki_world',X1: '$ki_world',X4: '$ki_world'] :
( open(X1,X2)
| ~ closed(X0,X2)
| ~ combo(X0,X2,X3)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_accessible'(X4,X0)
| ~ '$ki_accessible'('$ki_local_world',X4)
| ~ '$ki_accessible'(sK3,X0) )
| ~ spl5_1 ),
inference(resolution,[],[f76,f70]) ).
tff(f78,plain,
( ! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ closed(X0,d)
| ~ combo(X0,d,X1)
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_accessible'(X2,X0)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(sK3,X0) )
| ~ spl5_1
| spl5_5 ),
inference(resolution,[],[f77,f66]) ).
tff(f80,plain,
( ! [X2: '$ki_world',X0: '$ki_world'] :
( ~ closed(X0,d)
| ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_accessible'(X2,X0)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(sK3,X0) )
| ~ spl5_1
| ~ spl5_3
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f78,f71]) ).
tff(f81,plain,
( ! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,sK4)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(sK3,X0)
| ~ '$ki_accessible'('$ki_local_world',X0) )
| ~ spl5_1
| ~ spl5_3
| spl5_5 ),
inference(resolution,[],[f80,f37]) ).
tff(f83,plain,
( ! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(sK3,X0)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X0,sK4) )
| ~ spl5_1
| ~ spl5_3
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f81,f31]) ).
tff(f87,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK3,X0)
| ~ '$ki_accessible'('$ki_local_world',sK3)
| ~ '$ki_accessible'(X0,sK4) )
| ~ spl5_1
| ~ spl5_3
| spl5_5 ),
inference(factoring,[],[f83]) ).
tff(f88,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK3,X0)
| ~ '$ki_accessible'(X0,sK4) )
| ~ spl5_1
| ~ spl5_3
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f87,f42]) ).
tff(f99,plain,
( ~ '$ki_accessible'(sK4,sK4)
| ~ spl5_1
| ~ spl5_3
| ~ spl5_4
| spl5_5 ),
inference(resolution,[],[f88,f61]) ).
tff(f104,plain,
( $false
| ~ spl5_1
| ~ spl5_3
| ~ spl5_4
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f99,f30]) ).
tff(f105,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_4
| spl5_5 ),
inference(avatar_contradiction_clause,[],[f104]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f53]) ).
cnf(s2,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f57]) ).
cnf(s3,plain,
( spl5_2
| spl5_2
| spl5_4 ),
inference(sat_conversion,[],[f62]) ).
cnf(s4,plain,
( spl5_2
| spl5_4 ),
inference(rat,[],[s3]) ).
cnf(s5,plain,
( spl5_2
| spl5_2
| ~ spl5_5 ),
inference(sat_conversion,[],[f67]) ).
cnf(s6,plain,
( spl5_2
| ~ spl5_5 ),
inference(rat,[],[s5]) ).
cnf(s7,plain,
~ spl5_2,
inference(sat_conversion,[],[f69]) ).
cnf(s9,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f105]) ).
cnf(s10,plain,
~ spl5_5,
inference(rat,[],[s6,s7]) ).
cnf(s11,plain,
spl5_4,
inference(rat,[],[s4,s7]) ).
cnf(s12,plain,
spl5_3,
inference(rat,[],[s2,s7]) ).
cnf(s13,plain,
~ spl5_1,
inference(rat,[],[s9,s10,s11,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s7,s13]) ).
tff(f106,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA054_4 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 22:18:12 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.70/1.28 % (3268221)Detected formulas, will run a generic FOF schedule.
% 2.70/1.28 % (3268227)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=3727531253:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.70/1.28 % (3268230)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1009476867:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.70/1.28 % (3268231)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3289694756:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.70/1.28 % (3268229)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3854914123:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.70/1.28 % (3268228)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=1997767939:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.70/1.28 % (3268226)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=4026589222:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.70/1.28 % (3268232)dis-21_1_sil=8000:lcm=predicate:random_seed=4128729467: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)
% 2.70/1.28 % (3268229)Refutation not found, incomplete strategy
% 2.70/1.28 % (3268229)------------------------------
% 2.70/1.28 % (3268229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.28 % (3268230)Refutation not found, incomplete strategy
% 2.70/1.28 % (3268230)------------------------------
% 2.70/1.28 % (3268230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.28 % (3268230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.28 % (3268229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.28 % (3268230)CaDiCaL version: 2.1.3
% 2.70/1.28 % (3268230)Termination reason: Refutation not found, incomplete strategy
% 2.70/1.28 % (3268230)Time elapsed: 0.001 s
% 2.70/1.28 % (3268230)Peak memory usage: 88 MB
% 2.70/1.28 % (3268229)CaDiCaL version: 2.1.3
% 2.70/1.28 % (3268229)Termination reason: Refutation not found, incomplete strategy
% 2.70/1.28 % (3268229)Time elapsed: 0.001 s
% 2.70/1.28 % (3268229)Peak memory usage: 88 MB
% 2.70/1.28 % (3268231)First to succeed.
% 2.70/1.28 % (3268232)Also succeeded, but the first one will report.
% 2.70/1.28 % (3268231)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3268221"
% 2.70/1.28 % (3268229)------------------------------
% 2.70/1.28 % (3268229)------------------------------
% 2.70/1.28 % (3268230)------------------------------
% 2.70/1.28 % (3268230)------------------------------
% 2.70/1.28 % (3268231)Refutation found. Thanks to Tanya!
% 2.70/1.28 % SZS status Theorem for theBenchmark
% 2.70/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.43/1.47 % (3268231)------------------------------
% 3.43/1.47 % (3268231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.47 % (3268231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.47 % (3268231)CaDiCaL version: 2.1.3
% 3.43/1.47 % (3268231)Termination reason: Refutation
% 3.43/1.47 % (3268231)Time elapsed: 0.005 s
% 3.43/1.47 % (3268231)Peak memory usage: 90 MB
% 3.43/1.47 % (3268231)Instructions burned: 5 (million)
% 3.43/1.47 % (3268231)------------------------------
% 3.43/1.47 % (3268231)------------------------------
% 3.43/1.47 % (3268221)Success in time 0.399 s
% 3.43/1.47 % Vampire exiting
%------------------------------------------------------------------------------