%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYP048_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 09:51:46 AM UTC 2026
% Result : Theorem 8.01s 2.86s
% Output : Refutation 8.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 6 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 817 ( 0 equ; 0 cnn)
% Maximal formula atoms : 270 ( 136 avg)
% Number of connectives : 2175 ( 17 ~; 39 |; 188 &;1347 @)
% ( 0 <=>; 584 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 25 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 531 ( 0 ^; 393 !; 138 ?; 531 :)
% Comments :
%------------------------------------------------------------------------------
thf('$world_type',type,
'$world': $tType ).
thf('$local_world_decl',type,
'$local_world': '$world' ).
thf('$accessible_world_decl',type,
'$accessible_world': '$world' > '$world' > $o ).
thf(p0_decl,type,
p0: '$world' > $o ).
thf(1,conjecture,
( ( ~ ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) )
=> ( L @ p0 ) ) )
=> ( ? [L: '$world'] :
( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) )
& ( L @ ( K @ '$accessible_world' ) ) )
=> ( K @ p0 ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( ( G @ p0 )
=> ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ p0 ) ) ) )
=> ( F @ p0 ) ) )
=> ( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ p0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
=> ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) )
| ( E @ p0 ) ) ) )
& ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ p0 ) )
=> ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ p0 ) ) ) ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ( F @ p0 )
=> ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ p0 ) ) ) )
=> ( E @ p0 ) ) )
=> ( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
=> ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) )
| ( D @ p0 ) ) ) )
& ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) )
=> ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ p0 ) ) ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ( E @ p0 )
=> ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) ) ) )
=> ( D @ p0 ) ) )
=> ( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
=> ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) )
| ( C @ p0 ) ) ) )
& ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( D @ p0 )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) ) ) )
=> ( C @ p0 ) ) )
=> ( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ p0 ) )
| ( B @ p0 ) ) ) )
& ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( C @ p0 )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) ) ) )
=> ( B @ p0 ) ) )
=> ( ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ p0 ) )
& ( B @ ( A @ '$accessible_world' ) ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ p0 ) )
| ( A @ p0 ) ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ p0 ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) ) ) ) ) ) ) )
=> ( ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ~ ( ( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( ( K @ p0 )
=> ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( L @ p0 ) ) ) )
=> ( J @ p0 ) ) )
=> ( ? [J: '$world'] :
( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ p0 ) )
& ( J @ ( I @ '$accessible_world' ) ) )
=> ( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) )
| ( I @ p0 ) ) ) )
& ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ p0 ) )
=> ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( L @ p0 ) ) ) ) ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ~ ( ( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( ( J @ p0 )
=> ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ p0 ) ) ) )
=> ( I @ p0 ) ) )
=> ( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
=> ( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ p0 ) )
| ( H @ p0 ) ) ) )
& ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) )
=> ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ p0 ) ) ) ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ~ ( ( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( ( I @ p0 )
=> ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) ) ) )
=> ( H @ p0 ) ) )
=> ( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ p0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
=> ( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ p0 ) )
| ( G @ p0 ) ) ) )
& ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ p0 ) )
=> ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) ) ) ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ? [J: '$world'] :
( ? [K: '$world'] :
( ~ ( ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( ( N @ p0 )
=> ! [O: '$world'] :
( ( O @ ( N @ '$accessible_world' ) )
=> ( O @ p0 ) ) ) ) ) )
=> ( ( L @ p0 )
=> ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) ) ) ) )
=> ( ? [L: '$world'] :
( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) )
& ( L @ ( K @ '$accessible_world' ) ) )
=> ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ( L @ p0 )
=> ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) ) ) )
| ( ( K @ p0 )
=> ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( L @ p0 ) ) ) ) ) )
& ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) )
=> ( L @ p0 ) ) )
=> ( ? [L: '$world'] :
( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) )
& ( L @ ( K @ '$accessible_world' ) ) )
=> ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( L @ p0 ) )
| ( K @ p0 ) ) ) )
& ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) )
=> ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) ) )
& ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) )
=> ( L @ p0 ) ) )
=> ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( ( N @ p0 )
=> ! [O: '$world'] :
( ( O @ ( N @ '$accessible_world' ) )
=> ( O @ p0 ) ) ) )
=> ( M @ p0 ) ) ) ) ) )
& ( K @ ( J @ '$accessible_world' ) ) )
& ( J @ ( I @ '$accessible_world' ) ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',10) ).
thf(2,negated_conjecture,
~ ( ( ~ ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) )
=> ( L @ p0 ) ) )
=> ( ? [L: '$world'] :
( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) )
& ( L @ ( K @ '$accessible_world' ) ) )
=> ( K @ p0 ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( ( G @ p0 )
=> ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ p0 ) ) ) )
=> ( F @ p0 ) ) )
=> ( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ p0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
=> ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) )
| ( E @ p0 ) ) ) )
& ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ p0 ) )
=> ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ p0 ) ) ) ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ( F @ p0 )
=> ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ p0 ) ) ) )
=> ( E @ p0 ) ) )
=> ( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
=> ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) )
| ( D @ p0 ) ) ) )
& ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) )
=> ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ p0 ) ) ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ( E @ p0 )
=> ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) ) ) )
=> ( D @ p0 ) ) )
=> ( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
=> ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) )
| ( C @ p0 ) ) ) )
& ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( D @ p0 )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) ) ) )
=> ( C @ p0 ) ) )
=> ( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ p0 ) )
| ( B @ p0 ) ) ) )
& ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( C @ p0 )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) ) ) )
=> ( B @ p0 ) ) )
=> ( ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ p0 ) )
& ( B @ ( A @ '$accessible_world' ) ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ p0 ) )
| ( A @ p0 ) ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ p0 ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) ) ) ) ) ) ) )
=> ( ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ~ ( ( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( ( K @ p0 )
=> ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( L @ p0 ) ) ) )
=> ( J @ p0 ) ) )
=> ( ? [J: '$world'] :
( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ p0 ) )
& ( J @ ( I @ '$accessible_world' ) ) )
=> ( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) )
| ( I @ p0 ) ) ) )
& ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ p0 ) )
=> ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( L @ p0 ) ) ) ) ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ~ ( ( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( ( J @ p0 )
=> ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ p0 ) ) ) )
=> ( I @ p0 ) ) )
=> ( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
=> ( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ p0 ) )
| ( H @ p0 ) ) ) )
& ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) )
=> ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ p0 ) ) ) ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ~ ( ( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( ( I @ p0 )
=> ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) ) ) )
=> ( H @ p0 ) ) )
=> ( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ p0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
=> ( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ p0 ) )
| ( G @ p0 ) ) ) )
& ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ p0 ) )
=> ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) ) ) ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ? [J: '$world'] :
( ? [K: '$world'] :
( ~ ( ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( ( N @ p0 )
=> ! [O: '$world'] :
( ( O @ ( N @ '$accessible_world' ) )
=> ( O @ p0 ) ) ) ) ) )
=> ( ( L @ p0 )
=> ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) ) ) ) )
=> ( ? [L: '$world'] :
( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) )
& ( L @ ( K @ '$accessible_world' ) ) )
=> ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ( L @ p0 )
=> ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) ) ) )
| ( ( K @ p0 )
=> ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( L @ p0 ) ) ) ) ) )
& ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) )
=> ( L @ p0 ) ) )
=> ( ? [L: '$world'] :
( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) )
& ( L @ ( K @ '$accessible_world' ) ) )
=> ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( L @ p0 ) )
| ( K @ p0 ) ) ) )
& ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) )
=> ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) ) )
& ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) )
=> ( L @ p0 ) ) )
=> ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( ( N @ p0 )
=> ! [O: '$world'] :
( ( O @ ( N @ '$accessible_world' ) )
=> ( O @ p0 ) ) ) )
=> ( M @ p0 ) ) ) ) ) )
& ( K @ ( J @ '$accessible_world' ) ) )
& ( J @ ( I @ '$accessible_world' ) ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ( ( ~ ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) )
=> ( L @ p0 ) ) )
=> ( ? [L: '$world'] :
( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) )
& ( L @ ( K @ '$accessible_world' ) ) )
=> ( K @ p0 ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( ( G @ p0 )
=> ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ p0 ) ) ) )
=> ( F @ p0 ) ) )
=> ( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ p0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
=> ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) )
| ( E @ p0 ) ) ) )
& ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ p0 ) )
=> ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ p0 ) ) ) ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ( F @ p0 )
=> ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ p0 ) ) ) )
=> ( E @ p0 ) ) )
=> ( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
=> ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) )
| ( D @ p0 ) ) ) )
& ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) )
=> ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ p0 ) ) ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ( E @ p0 )
=> ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) ) ) )
=> ( D @ p0 ) ) )
=> ( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
=> ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) )
| ( C @ p0 ) ) ) )
& ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ p0 ) ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( D @ p0 )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) ) ) )
=> ( C @ p0 ) ) )
=> ( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ p0 ) )
| ( B @ p0 ) ) ) )
& ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ p0 ) ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( C @ p0 )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) ) ) )
=> ( B @ p0 ) ) )
=> ( ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ p0 ) )
& ( B @ ( A @ '$accessible_world' ) ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ p0 ) )
| ( A @ p0 ) ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ p0 ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ p0 ) ) ) ) ) ) ) )
=> ( ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ~ ( ( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( ( K @ p0 )
=> ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( L @ p0 ) ) ) )
=> ( J @ p0 ) ) )
=> ( ? [J: '$world'] :
( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ p0 ) )
& ( J @ ( I @ '$accessible_world' ) ) )
=> ( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) )
| ( I @ p0 ) ) ) )
& ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ p0 ) )
=> ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( L @ p0 ) ) ) ) ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ~ ( ( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( ( J @ p0 )
=> ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ p0 ) ) ) )
=> ( I @ p0 ) ) )
=> ( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
=> ( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ p0 ) )
| ( H @ p0 ) ) ) )
& ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) )
=> ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ p0 ) ) ) ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ~ ( ( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( ( I @ p0 )
=> ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) ) ) )
=> ( H @ p0 ) ) )
=> ( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ p0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
=> ( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ p0 ) )
| ( G @ p0 ) ) ) )
& ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ p0 ) )
=> ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ p0 ) ) ) ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ? [J: '$world'] :
( ? [K: '$world'] :
( ~ ( ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( ( N @ p0 )
=> ! [O: '$world'] :
( ( O @ ( N @ '$accessible_world' ) )
=> ( O @ p0 ) ) ) ) ) )
=> ( ( L @ p0 )
=> ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) ) ) ) )
=> ( ? [L: '$world'] :
( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) )
& ( L @ ( K @ '$accessible_world' ) ) )
=> ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ( L @ p0 )
=> ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) ) ) )
| ( ( K @ p0 )
=> ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( L @ p0 ) ) ) ) ) )
& ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) )
=> ( L @ p0 ) ) )
=> ( ? [L: '$world'] :
( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) )
& ( L @ ( K @ '$accessible_world' ) ) )
=> ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( L @ p0 ) )
| ( K @ p0 ) ) ) )
& ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( M @ p0 ) )
=> ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) ) )
& ( ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ( ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ( M @ p0 )
=> ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( N @ p0 ) ) ) )
=> ( L @ p0 ) ) )
=> ! [L: '$world'] :
( ( L @ ( K @ '$accessible_world' ) )
=> ! [M: '$world'] :
( ( M @ ( L @ '$accessible_world' ) )
=> ( ! [N: '$world'] :
( ( N @ ( M @ '$accessible_world' ) )
=> ( ( N @ p0 )
=> ! [O: '$world'] :
( ( O @ ( N @ '$accessible_world' ) )
=> ( O @ p0 ) ) ) )
=> ( M @ p0 ) ) ) ) ) )
& ( K @ ( J @ '$accessible_world' ) ) )
& ( J @ ( I @ '$accessible_world' ) ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '$world',B: '$world',C: '$world'] :
( ( ( B @ ( A @ '$accessible_world' ) )
& ( C @ ( A @ '$accessible_world' ) ) )
=> ( B @ ( C @ '$accessible_world' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_euclidean) ).
thf(187,plain,
! [A: '$world',B: '$world',C: '$world'] :
( ( ( B @ ( A @ '$accessible_world' ) )
& ( C @ ( A @ '$accessible_world' ) ) )
=> ( B @ ( C @ '$accessible_world' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(627,plain,
$false,
inference(e,[status(thm)],[4,187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYP048_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n002.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 20:27:21 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.69/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.92/0.83 % [INFO] Parsing done (111ms).
% 0.92/0.84 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 0.92/0.85 %%% First-order logic specification detected, trying modal-logic-to-TXF embedding (redirected from embedding '$$modal' to embedding '$$fomlModel' version 1.3.7) ... Use flag -p FORCE_HIGHERORDER if you want to have THF output instead.
% 1.24/0.91 % [INFO] Running in sequential loop mode.
% 1.73/1.11 % [INFO] eprover registered as external prover.
% 1.73/1.11 % [INFO] Scanning for conjecture ...
% 2.28/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.28/1.28 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.28/1.29 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.62/1.30 % [INFO] Type checking passed.
% 2.62/1.30 % [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 ...
% 8.01/2.86 % External prover 'e' found a proof!
% 8.01/2.86 % [INFO] Killing All external provers ...
% 8.01/2.86 % Time passed: 2364ms (effective reasoning time: 1949ms)
% 8.01/2.86 % 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)>
% 8.01/2.86 % Axioms used in derivation (1): mrel_euclidean
% 8.01/2.86 % No. of inferences in proof: 6
% 8.01/2.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2364 ms resp. 1949 ms w/o parsing
% 8.88/2.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.88/2.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------