%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL942^2 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 : Mon Sep 7 01:02:55 PM UTC 2026
% Result : Theorem 1.05s 1.52s
% Output : Proof 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 28
% Syntax : Number of formulae : 33 ( 16 unt; 0 typ; 11 def)
% Number of atoms : 548 ( 12 equ; 0 cnn)
% Maximal formula atoms : 67 ( 16 avg)
% Number of connectives : 2436 ( 198 ~; 8 |; 0 &;1732 @)
% ( 8 <=>; 490 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 26 con; 0-3 aty)
% Number of variables : 281 ( 24 ^; 257 !; 0 ?; 281 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_e0,type,
e0: $i ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(ty_e3,type,
e3: $i ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_e2,type,
e2: $i ).
thf(ty_e1,type,
e1: $i ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(ty_op,type,
op: $i > $i > $i ).
thf(h0,assumption,
! [X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ mactual @ X1 )
=> ( ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ) )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ) ) )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ) ) ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ( ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) ) ) ) )
=> ( ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ) )
=> ( ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ) )
=> ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( ( mrel @ mactual @ eigen__0 )
=> ( ( ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ) ) )
=> ( ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ) )
=> ( ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X1 ) ) ) ) )
=> ~ ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ) ) ) ) ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ) )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ) ) )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: mworld] : ( mrel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( mrel @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
=> ~ ( ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ) ) )
=> ( ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ) )
=> ( ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X1 ) ) ) ) )
=> ~ ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ) ) )
=> ( ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ) )
=> ( ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X1 ) ) ) ) )
=> ~ ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ) ) ) ) ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ) )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ) ) )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ) )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ) ) )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ) ) )
=> ( ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ) )
=> ( ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X1 ) ) ) ) )
=> ~ ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ) )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ) ) )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ) ) ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ( ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) ) ) ) )
=> ( ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ) )
=> ( ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ) )
=> ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(def_mlocal,definition,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ) ).
thf(def_mforall_di,definition,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_di,definition,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
~ ! [X3: $i] :
~ ( X1 @ X3 @ X2 ) ) ) ).
thf(co1,conjecture,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ~ ( ( ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ) )
=> ( ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ) ) )
=> ( ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ) ) ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ( ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) ) ) ) )
=> ( ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ) )
=> ( ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ) )
=> ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ) ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ sP8,
inference(assume_negation,[status(cth)],[co1]) ).
thf(1,plain,
( ~ sP4
| ~ sP3
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP6
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( sP5
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP5
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP1
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP8
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(mrel_reflexive,axiom,
sP2 ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,mrel_reflexive,h1]) ).
thf(9,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[8,h0]) ).
thf(0,theorem,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ~ ( ( ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ) )
=> ( ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ) ) )
=> ( ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
=> ~ ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ) ) ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ( ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) ) ) ) )
=> ( ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ) )
=> ( ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ) )
=> ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[8,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL942^2 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.36 % Computer : n028.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 4 16:01:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 1.05/1.52 % SZS status Theorem
% 1.05/1.52 % Mode: mode506
% 1.05/1.52 % Inferences: 19180
% 1.05/1.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------