%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NLP266_23 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:08:17 PM UTC 2026
% Result : Theorem 2.92s 1.23s
% Output : Refutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 388 ( 0 equ)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 447 ( 192 ~; 176 |; 53 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 78 ( 78 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 4 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-4 aty)
% Number of variables : 211 ( 184 !; 27 ?; 211 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_3,type,
sK0: '$ki_world' ).
tff(func_def_4,type,
sK1: ( $i * $i ) > '$ki_world' ).
tff(func_def_5,type,
sK2: ( $i * $i * $i * $i ) > '$ki_world' ).
tff(func_def_7,type,
sK4: '$ki_world' > $i ).
tff(func_def_9,type,
sK6: ( '$ki_world' * $i * $i * $i ) > $i ).
tff(func_def_10,type,
sK7: '$ki_world' > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
number: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_3,type,
string: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
in: ( '$ki_world' * $i * $i * $i ) > $o ).
tff(pred_def_5,type,
do: ( '$ki_world' * $i * $i * $i ) > $o ).
tff(pred_def_6,type,
entry_box: ( '$ki_world' * $i ) > $o ).
tff(pred_def_7,type,
userid: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_8,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f1,axiom,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
tff(f2,axiom,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f4,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ( userid(X2,u,X1)
& string(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(f5,axiom,
? [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( entry_box(X1,X0)
& number(X1,X0,one) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(f6,axiom,
! [X0: '$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)
=> ( ( string(X0,X2)
& entry_box(X0,X3) )
=> ? [X4: $i] :
( '$ki_exists_in_world_$i'(X0,X4)
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ! [X6: $i] :
( '$ki_exists_in_world_$i'(X5,X6)
=> ( do(X5,X1,X4,X6)
=> in(X5,X2,X3,X6) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f7,conjecture,
! [X0: '$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: $i] :
( '$ki_exists_in_world_$i'(X0,X3)
& ? [X4: $i] :
( '$ki_exists_in_world_$i'(X0,X4)
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ( userid(X5,u,X1)
& entry_box(X5,X2)
& number(X5,X2,one) ) )
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ! [X6: $i] :
( '$ki_exists_in_world_$i'(X5,X6)
=> ( do(X5,X4,X3,X6)
=> in(X5,X1,X2,X6) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f8,negated_conjecture,
~ ! [X0: '$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: $i] :
( '$ki_exists_in_world_$i'(X0,X3)
& ? [X4: $i] :
( '$ki_exists_in_world_$i'(X0,X4)
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ( userid(X5,u,X1)
& entry_box(X5,X2)
& number(X5,X2,one) ) )
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ! [X6: $i] :
( '$ki_exists_in_world_$i'(X5,X6)
=> ( do(X5,X4,X3,X6)
=> in(X5,X1,X2,X6) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
tff(f9,plain,
~ ! [X0: '$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: $i] :
( '$ki_exists_in_world_$i'(X0,X4)
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X0,X5)
=> ( userid(X5,u,X1)
& entry_box(X5,X2)
& number(X5,X2,one) ) )
& ! [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
=> ! [X7: $i] :
( '$ki_exists_in_world_$i'(X6,X7)
=> ( do(X6,X4,X3,X7)
=> in(X6,X1,X2,X7) ) ) ) ) ) ) ) ),
inference(rectify,[],[f8]) ).
tff(f10,plain,
? [X0: '$ki_world'] :
( ! [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: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X4)
| ? [X5: '$ki_world'] :
( ( ~ userid(X5,u,X1)
| ~ entry_box(X5,X2)
| ~ number(X5,X2,one) )
& '$ki_accessible'(X0,X5) )
| ? [X6: '$ki_world'] :
( ? [X7: $i] :
( ~ in(X6,X1,X2,X7)
& do(X6,X4,X3,X7)
& '$ki_exists_in_world_$i'(X6,X7) )
& '$ki_accessible'(X0,X6) ) ) ) ) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f11,plain,
? [X0: '$ki_world'] :
( ! [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: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X4)
| ? [X5: '$ki_world'] :
( ( ~ userid(X5,u,X1)
| ~ entry_box(X5,X2)
| ~ number(X5,X2,one) )
& '$ki_accessible'(X0,X5) )
| ? [X6: '$ki_world'] :
( ? [X7: $i] :
( ~ in(X6,X1,X2,X7)
& do(X6,X4,X3,X7)
& '$ki_exists_in_world_$i'(X6,X7) )
& '$ki_accessible'(X0,X6) ) ) ) ) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f10]) ).
tff(f12,plain,
! [X0: '$ki_world'] :
( ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2: '$ki_world'] :
( ( userid(X2,u,X1)
& string(X2,X1) )
| ~ '$ki_accessible'(X0,X2) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f4]) ).
tff(f13,plain,
? [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( ( entry_box(X1,X0)
& number(X1,X0,one) )
| ~ '$ki_accessible'('$ki_local_world',X1) ) ),
inference(ennf_transformation,[],[f5]) ).
tff(f14,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ? [X4: $i] :
( '$ki_exists_in_world_$i'(X0,X4)
& ! [X5: '$ki_world'] :
( ! [X6: $i] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,X4,X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'(X0,X5) ) )
| ~ string(X0,X2)
| ~ entry_box(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X3) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f6]) ).
tff(f15,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ? [X4: $i] :
( '$ki_exists_in_world_$i'(X0,X4)
& ! [X5: '$ki_world'] :
( ! [X6: $i] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,X4,X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'(X0,X5) ) )
| ~ string(X0,X2)
| ~ entry_box(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X3) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(flattening,[],[f14]) ).
tff(f16,plain,
( ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X1)
| ! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X2)
| ! [X3: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X3)
| ! [X4: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X4)
| ( ( ~ userid(sK1(X1,X2),u,X1)
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one) )
& '$ki_accessible'(sK0,sK1(X1,X2)) )
| ( ~ in(sK2(X1,X2,X3,X4),X1,X2,sK3(X1,X2,X3,X4))
& do(sK2(X1,X2,X3,X4),X4,X3,sK3(X1,X2,X3,X4))
& '$ki_exists_in_world_$i'(sK2(X1,X2,X3,X4),sK3(X1,X2,X3,X4))
& '$ki_accessible'(sK0,sK2(X1,X2,X3,X4)) ) ) ) ) )
& '$ki_accessible'('$ki_local_world',sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X5,sK1(X1,X2)),skolemize(X6,sK2(X1,X2,X3,X4)),skolemize(X7,sK3(X1,X2,X3,X4))],[f11]) ).
tff(f17,plain,
! [X0: '$ki_world'] :
( ( '$ki_exists_in_world_$i'(X0,sK4(X0))
& ! [X2: '$ki_world'] :
( ( userid(X2,u,sK4(X0))
& string(X2,sK4(X0)) )
| ~ '$ki_accessible'(X0,X2) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f12]) ).
tff(f18,plain,
( '$ki_exists_in_world_$i'('$ki_local_world',sK5)
& ! [X1: '$ki_world'] :
( ( entry_box(X1,sK5)
& number(X1,sK5,one) )
| ~ '$ki_accessible'('$ki_local_world',X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X0,sK5)],[f13]) ).
tff(f19,plain,
! [X0: '$ki_world'] :
( ! [X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( '$ki_exists_in_world_$i'(X0,sK6(X0,X1,X2,X3))
& ! [X5: '$ki_world'] :
( ! [X6: $i] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK6(X0,X1,X2,X3),X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'(X0,X5) ) )
| ~ string(X0,X2)
| ~ entry_box(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X3) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X4,sK6(X0,X1,X2,X3))],[f15]) ).
tff(f28,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X1)
| ~ '$ki_exists_in_world_$i'(sK0,X2)
| ~ '$ki_exists_in_world_$i'(sK0,X3)
| ~ '$ki_exists_in_world_$i'(sK0,X4)
| ~ userid(sK1(X1,X2),u,X1)
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one)
| do(sK2(X1,X2,X3,X4),X4,X3,sK3(X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f16]) ).
tff(f29,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X1)
| ~ '$ki_exists_in_world_$i'(sK0,X2)
| ~ '$ki_exists_in_world_$i'(sK0,X3)
| ~ '$ki_exists_in_world_$i'(sK0,X4)
| ~ userid(sK1(X1,X2),u,X1)
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one)
| ~ in(sK2(X1,X2,X3,X4),X1,X2,sK3(X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f16]) ).
tff(f30,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f1]) ).
tff(f31,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( string(X2,sK4(X0))
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f17]) ).
tff(f32,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( userid(X2,u,sK4(X0))
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f17]) ).
tff(f34,plain,
! [X1: '$ki_world'] :
( number(X1,sK5,one)
| ~ '$ki_accessible'('$ki_local_world',X1) ),
inference(cnf_transformation,[],[f18]) ).
tff(f35,plain,
! [X1: '$ki_world'] :
( entry_box(X1,sK5)
| ~ '$ki_accessible'('$ki_local_world',X1) ),
inference(cnf_transformation,[],[f18]) ).
tff(f37,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK6(X0,X1,X2,X3),X6)
| ~ '$ki_exists_in_world_$i'(X5,X6)
| ~ '$ki_accessible'(X0,X5)
| ~ string(X0,X2)
| ~ entry_box(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f19]) ).
tff(f40,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f2]) ).
tff(f41,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X2)
| ~ '$ki_exists_in_world_$i'(sK0,X3)
| ~ '$ki_exists_in_world_$i'(sK0,X4)
| ~ userid(sK1(X1,X2),u,X1)
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one)
| do(sK2(X1,X2,X3,X4),X4,X3,sK3(X1,X2,X3,X4)) ),
inference(forward_subsumption_resolution,[],[f28,f40]) ).
tff(f42,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X3)
| ~ '$ki_exists_in_world_$i'(sK0,X4)
| ~ userid(sK1(X1,X2),u,X1)
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one)
| do(sK2(X1,X2,X3,X4),X4,X3,sK3(X1,X2,X3,X4)) ),
inference(forward_subsumption_resolution,[],[f41,f40]) ).
tff(f43,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X4)
| ~ userid(sK1(X1,X2),u,X1)
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one)
| do(sK2(X1,X2,X3,X4),X4,X3,sK3(X1,X2,X3,X4)) ),
inference(forward_subsumption_resolution,[],[f42,f40]) ).
tff(f44,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( do(sK2(X1,X2,X3,X4),X4,X3,sK3(X1,X2,X3,X4))
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one)
| ~ userid(sK1(X1,X2),u,X1) ),
inference(forward_subsumption_resolution,[],[f43,f40]) ).
tff(f45,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X2)
| ~ '$ki_exists_in_world_$i'(sK0,X3)
| ~ '$ki_exists_in_world_$i'(sK0,X4)
| ~ userid(sK1(X1,X2),u,X1)
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one)
| ~ in(sK2(X1,X2,X3,X4),X1,X2,sK3(X1,X2,X3,X4)) ),
inference(forward_subsumption_resolution,[],[f29,f40]) ).
tff(f46,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X3)
| ~ '$ki_exists_in_world_$i'(sK0,X4)
| ~ userid(sK1(X1,X2),u,X1)
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one)
| ~ in(sK2(X1,X2,X3,X4),X1,X2,sK3(X1,X2,X3,X4)) ),
inference(forward_subsumption_resolution,[],[f45,f40]) ).
tff(f47,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ '$ki_exists_in_world_$i'(sK0,X4)
| ~ userid(sK1(X1,X2),u,X1)
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one)
| ~ in(sK2(X1,X2,X3,X4),X1,X2,sK3(X1,X2,X3,X4)) ),
inference(forward_subsumption_resolution,[],[f46,f40]) ).
tff(f48,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ~ in(sK2(X1,X2,X3,X4),X1,X2,sK3(X1,X2,X3,X4))
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one)
| ~ userid(sK1(X1,X2),u,X1) ),
inference(forward_subsumption_resolution,[],[f47,f40]) ).
tff(f49,plain,
! [X1: '$ki_world'] : entry_box(X1,sK5),
inference(forward_subsumption_resolution,[],[f35,f30]) ).
tff(f50,plain,
! [X1: '$ki_world'] : number(X1,sK5,one),
inference(forward_subsumption_resolution,[],[f34,f30]) ).
tff(f51,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( string(X2,sK4(X0))
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f31,f30]) ).
tff(f52,plain,
! [X2: '$ki_world',X0: '$ki_world'] : string(X2,sK4(X0)),
inference(forward_subsumption_resolution,[],[f51,f30]) ).
tff(f53,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( userid(X2,u,sK4(X0))
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f32,f30]) ).
tff(f54,plain,
! [X2: '$ki_world',X0: '$ki_world'] : userid(X2,u,sK4(X0)),
inference(forward_subsumption_resolution,[],[f53,f30]) ).
tff(f55,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK6(X0,X1,X2,X3),X6)
| ~ '$ki_accessible'(X0,X5)
| ~ string(X0,X2)
| ~ entry_box(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f37,f40]) ).
tff(f56,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK6(X0,X1,X2,X3),X6)
| ~ string(X0,X2)
| ~ entry_box(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f55,f30]) ).
tff(f57,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK6(X0,X1,X2,X3),X6)
| ~ string(X0,X2)
| ~ entry_box(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f56,f40]) ).
tff(f58,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK6(X0,X1,X2,X3),X6)
| ~ string(X0,X2)
| ~ entry_box(X0,X3)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f57,f40]) ).
tff(f59,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( in(X5,X2,X3,X6)
| ~ do(X5,X1,sK6(X0,X1,X2,X3),X6)
| ~ string(X0,X2)
| ~ entry_box(X0,X3)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(forward_subsumption_resolution,[],[f58,f40]) ).
tff(f60,plain,
! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
( ~ do(X5,X1,sK6(X0,X1,X2,X3),X6)
| in(X5,X2,X3,X6)
| ~ string(X0,X2)
| ~ entry_box(X0,X3) ),
inference(forward_subsumption_resolution,[],[f59,f30]) ).
tff(f61,plain,
! [X2: '$ki_world',X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( in(sK2(X0,X1,sK6(X2,X3,X4,X5),X3),X4,X5,sK3(X0,X1,sK6(X2,X3,X4,X5),X3))
| ~ string(X2,X4)
| ~ entry_box(X2,X5)
| ~ entry_box(sK1(X0,X1),X1)
| ~ number(sK1(X0,X1),X1,one)
| ~ userid(sK1(X0,X1),u,X0) ),
inference(resolution,[],[f60,f44]) ).
tff(f63,plain,
! [X2: $i,X0: '$ki_world',X1: $i] :
( ~ string(X0,X1)
| ~ entry_box(X0,X2)
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one)
| ~ userid(sK1(X1,X2),u,X1)
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one)
| ~ userid(sK1(X1,X2),u,X1) ),
inference(resolution,[],[f61,f48]) ).
tff(f65,plain,
! [X2: $i,X0: '$ki_world',X1: $i] :
( ~ userid(sK1(X1,X2),u,X1)
| ~ entry_box(X0,X2)
| ~ entry_box(sK1(X1,X2),X2)
| ~ number(sK1(X1,X2),X2,one)
| ~ string(X0,X1) ),
inference(duplicate_literal_removal,[],[f63]) ).
tff(f66,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ entry_box(X0,X1)
| ~ entry_box(sK1(sK4(X2),X1),X1)
| ~ number(sK1(sK4(X2),X1),X1,one)
| ~ string(X0,sK4(X2)) ),
inference(resolution,[],[f65,f54]) ).
tff(f67,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ number(sK1(sK4(X2),X1),X1,one)
| ~ entry_box(sK1(sK4(X2),X1),X1)
| ~ entry_box(X0,X1) ),
inference(forward_subsumption_resolution,[],[f66,f52]) ).
tff(f68,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ entry_box(sK1(sK4(X0),sK5),sK5)
| ~ entry_box(X1,sK5) ),
inference(resolution,[],[f67,f50]) ).
tff(f69,plain,
! [X1: '$ki_world'] : ~ entry_box(X1,sK5),
inference(forward_subsumption_resolution,[],[f68,f49]) ).
tff(f70,plain,
$false,
inference(forward_subsumption_resolution,[],[f69,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NLP266_23 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.36 % Computer : n014.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sun Sep 27 18:38:32 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.39 Running first-order theorem proving
% 0.07/0.39 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.92/1.23 % (1093058)Detected formulas, will run a generic FOF schedule.
% 2.92/1.23 % (1093066)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4024347450:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.92/1.23 % (1093066)Refutation not found, incomplete strategy
% 2.92/1.23 % (1093066)------------------------------
% 2.92/1.23 % (1093066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.23 % (1093066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.23 % (1093066)CaDiCaL version: 2.1.3
% 2.92/1.23 % (1093066)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.23 % (1093066)Time elapsed: 0.002 s
% 2.92/1.23 % (1093066)Peak memory usage: 88 MB
% 2.92/1.23 % (1093066)Instructions burned: 4 (million)
% 2.92/1.23 % (1093069)dis-21_1_sil=8000:lcm=predicate:random_seed=80054354: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)
% 2.92/1.23 % (1093067)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2080348168:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.92/1.23 % (1093063)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=1998729210:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.92/1.23 % (1093064)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=2155661835:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.92/1.23 % (1093065)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=2447869343:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.92/1.23 % (1093067)First to succeed.
% 2.92/1.23 % (1093067)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1093058"
% 2.92/1.23 % (1093069)Also succeeded, but the first one will report.
% 2.92/1.23 % (1093068)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=481856005:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.92/1.23 % (1093068)Also succeeded, but the first one will report.
% 2.92/1.23 % (1093066)------------------------------
% 2.92/1.23 % (1093066)------------------------------
% 2.92/1.23 % (1093077)lrs+10_1_sil=8000:sp=occurrence:random_seed=3937108348:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.92/1.23 % (1093077)Also succeeded, but the first one will report.
% 2.92/1.23 % (1093067)Refutation found. Thanks to Tanya!
% 2.92/1.23 % SZS status Theorem for theBenchmark
% 2.92/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.33/1.33 % (1093067)------------------------------
% 3.33/1.33 % (1093067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.33 % (1093067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.33 % (1093067)CaDiCaL version: 2.1.3
% 3.33/1.33 % (1093067)Termination reason: Refutation
% 3.33/1.33 % (1093067)Time elapsed: 0.004 s
% 3.33/1.33 % (1093067)Peak memory usage: 88 MB
% 3.33/1.33 % (1093067)Instructions burned: 5 (million)
% 3.33/1.33 % (1093067)------------------------------
% 3.33/1.33 % (1093067)------------------------------
% 3.33/1.33 % (1093058)Success in time 0.405 s
% 3.33/1.33 % Vampire exiting
%------------------------------------------------------------------------------