TSTP Solution File: ALG017^7 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ALG017^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:32:57 EDT 2023
% Result : Theorem 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mu,type,
mu: $tType ).
thf(ty_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(ty_op,type,
op: mu > mu > mu ).
thf(ty_e3,type,
e3: mu ).
thf(ty_e0,type,
e0: mu ).
thf(ty_e1,type,
e1: mu ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(ty_e2,type,
e2: mu ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( rel_s4 @ eigen__1 @ eigen__1 )
=> ~ ( ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ) ) )
=> ( ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ) )
=> ( ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X1 ) ) ) ) )
=> ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
=> ( sP1
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
=> ( sP4
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X1 ) ) ) ) )
=> ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
=> ( sP1
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
=> ~ sP8 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP5
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP1
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
=> ~ sP8 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
=> ( sP4
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP13
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP7
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP14
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 ) )
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP21
=> ( sP11
=> sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP4
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( rel_s4 @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] : ( rel_s4 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ) )
=> ( ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ) ) )
=> ( ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP29
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP11
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mreflexive,definition,
( mreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_mtransitive,definition,
( mtransitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
@ ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( (~) @ ( rel_s4 @ X2 @ X3 ) )
| ( X1 @ X3 ) ) ) ) ).
thf(co1,conjecture,
! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ( ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) ) ) ) )
=> ( ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ) )
=> ( ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ) ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X4 ) ) ) ) )
=> ( ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) ) ) )
=> ( ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ) )
=> ~ ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ( ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) ) ) ) )
=> ( ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ) )
=> ( ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ) ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X4 ) ) ) ) )
=> ( ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) ) ) )
=> ( ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ) )
=> ~ ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
thf(h1,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__0 @ X1 )
=> ( ( ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ) )
=> ( ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ) ) )
=> ( ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ) ) ) ) ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) ) ) ) )
=> ( ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ) )
=> ( ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ( rel_s4 @ eigen__0 @ eigen__1 )
=> ( sP22
=> ~ sP33 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
rel_s4 @ eigen__0 @ eigen__1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP22
=> ~ sP33 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP22,
introduced(assumption,[]) ).
thf(h6,assumption,
sP33,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP21,
introduced(assumption,[]) ).
thf(h8,assumption,
sP35,
introduced(assumption,[]) ).
thf(h9,assumption,
sP24,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h11,assumption,
sP7,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h13,assumption,
sP6,
introduced(assumption,[]) ).
thf(h14,assumption,
sP9,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| ~ sP6
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP18
| ~ sP7
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP21
| ~ sP24
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP22
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| ~ sP25
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP33
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP27
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(a1,axiom,
sP27 ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,h9,h11,h13,h14,h6,a1]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,8,h13,h14]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,9,h11,h12]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,10,h9,h10]) ).
thf(h15,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h16,assumption,
sP10,
introduced(assumption,[]) ).
thf(h17,assumption,
sP5,
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h19,assumption,
sP13,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h21,assumption,
sP26,
introduced(assumption,[]) ).
thf(h22,assumption,
sP31,
introduced(assumption,[]) ).
thf(12,plain,
( ~ sP15
| ~ sP26
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP17
| ~ sP13
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP11
| ~ sP5
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP35
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP22
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP2
| ~ sP25
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP33
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP27
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h15,h8,h5,h6,h3,h4,h2,h1,h0])],[12,13,14,15,16,17,18,19,h17,h19,h21,h22,h6,a1]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,20,h21,h22]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,21,h19,h20]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,22,h17,h18]) ).
thf(h23,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h24,assumption,
~ sP34,
introduced(assumption,[]) ).
thf(h25,assumption,
sP32,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(h27,assumption,
sP4,
introduced(assumption,[]) ).
thf(h28,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h29,assumption,
sP28,
introduced(assumption,[]) ).
thf(h30,assumption,
sP30,
introduced(assumption,[]) ).
thf(24,plain,
( ~ sP19
| ~ sP28
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP23
| ~ sP4
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP16
| ~ sP32
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP10
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP35
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP22
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP2
| ~ sP25
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP33
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP27
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h29,h30,h27,h28,h25,h26,h23,h16,h8,h5,h6,h3,h4,h2,h1,h0])],[24,25,26,27,28,29,30,31,32,h25,h27,h29,h30,h6,a1]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h28,h25,h26,h23,h16,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h28,33,h29,h30]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h26,h23,h16,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,34,h27,h28]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h16,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h25,h26])],[h23,35,h25,h26]) ).
thf(h31,assumption,
sP29,
introduced(assumption,[]) ).
thf(h32,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h33,assumption,
sP1,
introduced(assumption,[]) ).
thf(h34,assumption,
~ sP20,
introduced(assumption,[]) ).
thf(h35,assumption,
sP14,
introduced(assumption,[]) ).
thf(h36,assumption,
sP8,
introduced(assumption,[]) ).
thf(37,plain,
( ~ sP20
| ~ sP14
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP12
| ~ sP1
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP34
| ~ sP29
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP10
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP35
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP22
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP2
| ~ sP25
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP27
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP33
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h35,h36,h33,h34,h31,h32,h24,h16,h8,h5,h6,h3,h4,h2,h1,h0])],[37,38,39,40,41,42,43,44,45,h31,h33,h35,h36,h6,a1]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h34,h31,h32,h24,h16,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h35,h36])],[h34,46,h35,h36]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h32,h24,h16,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h33,h34])],[h32,47,h33,h34]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h16,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h24,48,h31,h32]) ).
thf(50,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h16,h8,h5,h6,h3,h4,h2,h1,h0]),tab_imp(discharge,[h23]),tab_imp(discharge,[h24])],[h16,36,49,h23,h24]) ).
thf(51,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h5,h6,h3,h4,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h8,23,50,h15,h16]) ).
thf(52,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,11,51,h7,h8]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,52,h5,h6]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,53,h3,h4]) ).
thf(55,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,54,h2]) ).
thf(56,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,55,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ( ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) ) ) ) )
=> ( ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ) )
=> ( ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ) ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X4 ) ) ) ) )
=> ( ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) ) ) )
=> ( ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ) )
=> ~ ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[56,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG017^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 02:54:34 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 % Mode: cade22sinegrackle2x6978
% 0.20/0.49 % Steps: 1013
% 0.20/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------