%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL947_10 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 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 : Sun Sep 27 07:53:26 AM UTC 2026
% Result : Theorem 8.01s 3.34s
% Output : Refutation 8.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 42 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 453 ( 0 equ; 0 cnn)
% Maximal formula atoms : 34 ( 10 avg)
% Number of connectives : 1470 ( 2 ~; 4 |; 28 &;1057 @)
% ( 0 <=>; 379 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 17 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 343 ( 0 ^; 341 !; 2 ?; 343 :)
% Comments :
%------------------------------------------------------------------------------
thf('$ki_world_type',type,
'$ki_world': $tType ).
thf('$ki_local_world_decl',type,
'$ki_local_world': '$ki_world' ).
thf('$ki_accessible_decl',type,
'$ki_accessible': '$ki_world' > '$ki_world' > $o ).
thf(qmltpeq_decl,type,
qmltpeq: '$ki_world' > $i > $i > $o ).
thf(member_decl,type,
member: '$ki_world' > $i > $i > $o ).
thf(subset_decl,type,
subset: '$ki_world' > $i > $i > $o ).
thf(union_decl,type,
union: $i > $i > $i ).
thf('$ki_exists_in_world_$i_decl',type,
'$ki_exists_in_world_$i': '$ki_world' > $i > $o ).
thf(15,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ union ) @ ( F @ ( B @ union ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_1) ).
thf(120,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ union ) @ ( F @ ( B @ union ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subset ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subset ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(142,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subset ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subset ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(18,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( C @ subset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(134,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ member ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_1) ).
thf(98,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ member ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ subset ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ subset ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_1) ).
thf(108,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ subset ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ subset ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).
thf(48,plain,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) ) ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
thf(50,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) ) ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subset ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( D @ ( B @ union ) @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_union) ).
thf(104,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subset ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( D @ ( B @ union ) @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(114,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ subset ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ subset ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_2) ).
thf(136,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ subset ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ subset ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [A: '$ki_world',B: '$ki_world',C: '$ki_world'] :
( ( ( C @ ( B @ '$ki_accessible' ) )
& ( B @ ( A @ '$ki_accessible' ) ) )
=> ( C @ ( A @ '$ki_accessible' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
thf(28,plain,
! [A: '$ki_world',B: '$ki_world',C: '$ki_world'] :
( ( ( C @ ( B @ '$ki_accessible' ) )
& ( B @ ( A @ '$ki_accessible' ) ) )
=> ( C @ ( A @ '$ki_accessible' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,axiom,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(160,plain,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_2) ).
thf(124,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ union ) @ ( D @ ( B @ union ) @ ( E @ qmltpeq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(96,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ union ) @ ( D @ ( B @ union ) @ ( E @ qmltpeq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( B @ union ) @ ( C @ qmltpeq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( B @ union ) @ ( C @ qmltpeq ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( B @ union ) @ ( C @ qmltpeq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( C @ qmltpeq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(118,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( C @ qmltpeq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ union ) @ ( B @ ( F @ union ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_2) ).
thf(130,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ union ) @ ( B @ ( F @ union ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(8,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ subset ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subset ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ subset ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subset ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(80,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ subset ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subset ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ subset ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subset ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ( ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) )
| ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ union ) @ ( F @ ( H @ member ) ) ) ) ) )
& ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ union ) @ ( F @ ( H @ member ) ) ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) )
| ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
thf(36,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ( ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) )
| ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ union ) @ ( F @ ( H @ member ) ) ) ) ) )
& ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ union ) @ ( F @ ( H @ member ) ) ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) )
| ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ qmltpeq ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(30,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ qmltpeq ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(239,plain,
$false,
inference(e,[status(thm)],[120,142,134,98,108,48,50,104,114,136,28,160,124,96,22,118,130,80,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL947_10 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/0.41 % Computer : n015.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Fri Sep 25 23:54:28 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.70/0.72 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.96 % [INFO] Parsing done (237ms).
% 1.22/0.97 % [INFO] Running in sequential loop mode.
% 2.13/1.35 % [INFO] eprover registered as external prover.
% 2.13/1.36 % [INFO] Scanning for conjecture ...
% 2.37/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 2.56/1.58 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 3.08/1.72 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.08/1.75 % [INFO] Type checking passed.
% 3.08/1.76 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 8.01/3.34 % External prover 'e' found a proof!
% 8.01/3.34 % [INFO] Killing All external provers ...
% 8.01/3.34 % Time passed: 2835ms (effective reasoning time: 2359ms)
% 8.01/3.34 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.01/3.34 % Axioms used in derivation (19): member_substitution_1, equal_member_defn, union_substitution_2, subset_union, member_substitution_2, symmetry, reflexivity_of_subset, $ki_exists_in_world_$i_nonempty, mrel_reflexive, subset_substitution_2, reflexivity, commutativity_of_union, subset_substitution_1, union_substitution_1, mrel_transitive, equal_defn, transitivity, union_defn, subset_defn
% 8.01/3.34 % No. of inferences in proof: 42
% 8.01/3.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2835 ms resp. 2359 ms w/o parsing
% 8.47/3.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.47/3.43 % [INFO] Killing All external provers ...
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