%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU704^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n021.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 : Thu Oct 9 02:34:10 PM UTC 2025
% Result : Theorem 22.60s 22.82s
% Output : Proof 22.60s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__1,type,
eigen__1: $o ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ X1
=> ( in @ X3
@ ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( in @ eigen__2 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ eigen__1
=> ( ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X2
=> ( in @ X4
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( in @ eigen__3
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( in @ eigen__2
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) )
!= ( setadjoin @ eigen__2 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ eigen__1
=> ( in @ X1
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( in @ eigen__2
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP1
=> ( eigen__1
=> ( ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) )
= ( setadjoin @ eigen__2 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X2
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP1
=> ( ~ eigen__1
=> sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( in @ eigen__2 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__1
=> ( ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) )
= ( setadjoin @ eigen__2 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__1
=> ( in @ eigen__2
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__1
=> ( ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) )
= ( setadjoin @ eigen__2 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP1
=> ( eigen__1
=> sP8 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) )
= ( setadjoin @ eigen__2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ eigen__1
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X2
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) )
= ( setadjoin @ X4 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ eigen__1
=> ( ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__1
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__1
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) )
= ( setadjoin @ eigen__3 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X1
=> ( in @ X2
@ ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ eigen__1
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( in @ eigen__2 @ eigen__0 )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> eigen__1 ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP5
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ sP26
=> ( ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP26
=> ( X3 != X1 ) )
=> ~ ( ~ sP26
=> ( X3 != X2 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ X1
=> ( ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( sP26
=> ( X2 != eigen__2 ) )
=> ~ ( ~ sP26
=> ( X2 != eigen__3 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( sP26
=> ( X2 != eigen__2 ) )
=> ~ ( ~ sP26
=> ( X2 != eigen__3 ) ) ) )
!= ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( sP26
=> ( ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP26
=> ( X3 != X1 ) )
=> ~ ( ~ sP26
=> ( X3 != X2 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP30
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X1
=> ( ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( sP26
=> ( in @ X1
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP26
=> ( X3 != X1 ) )
=> ~ ( ~ sP26
=> ( X3 != X2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ sP26
=> ( in @ X2
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP26
=> ( X3 != X1 ) )
=> ~ ( ~ sP26
=> ( X3 != X2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP1
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X2
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).
thf(def_iffalseProp1,definition,
( iffalseProp1
= ( ! [X1: $i,X2: $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( (~) @ X2 )
@ ( in @ X4
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
& ( X5 = X3 ) )
| ( ( (~) @ X2 )
& ( X5 = X4 ) ) ) ) ) ) ) ) ) ) ).
thf(def_iffalseProp2,definition,
( iffalseProp2
= ( ! [X1: $i,X2: $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( (~) @ X2 )
@ ( ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
& ( X5 = X3 ) )
| ( ( (~) @ X2 )
& ( X5 = X4 ) ) ) )
= ( setadjoin @ X4 @ emptyset ) ) ) ) ) ) ) ).
thf(def_iftrueProp1,definition,
( iftrueProp1
= ( ! [X1: $i,X2: $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ X2
@ ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
& ( X5 = X3 ) )
| ( ( (~) @ X2 )
& ( X5 = X4 ) ) ) ) ) ) ) ) ) ) ).
thf(def_iftrueProp2,definition,
( iftrueProp2
= ( ! [X1: $i,X2: $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ X2
@ ( ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
& ( X5 = X3 ) )
| ( ( (~) @ X2 )
& ( X5 = X4 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ).
thf(ifSingleton,conjecture,
( sP4
=> ( sP18
=> ( sP10
=> ( sP38
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP4
=> ( sP18
=> ( sP10
=> ( sP38
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[ifSingleton]) ).
thf(h1,assumption,
sP4,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP18
=> ( sP10
=> ( sP38
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP18,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP10
=> ( sP38
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP10,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP38
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP38,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ~ ! [X4: $i] :
( ( in @ X4
@ ( dsetconstr @ eigen__0
@ ^ [X5: $i] :
( ( X1
=> ( X5 != X2 ) )
=> ~ ( ~ X1
=> ( X5 != X3 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X5: $i] :
( ( X1
=> ( X5 != X2 ) )
=> ~ ( ~ X1
=> ( X5 != X3 ) ) ) )
!= ( setadjoin @ X4 @ emptyset ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ~ ! [X3: $i] :
( ( in @ X3
@ ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( sP26
=> ( X4 != X1 ) )
=> ~ ( ~ sP26
=> ( X4 != X2 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( sP26
=> ( X4 != X1 ) )
=> ~ ( ~ sP26
=> ( X4 != X2 ) ) ) )
!= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP30
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP26
=> ( X3 != eigen__2 ) )
=> ~ ( ~ sP26
=> ( X3 != X1 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP26
=> ( X3 != eigen__2 ) )
=> ~ ( ~ sP26
=> ( X3 != X1 ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP30,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP26
=> ( X3 != eigen__2 ) )
=> ~ ( ~ sP26
=> ( X3 != X1 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP26
=> ( X3 != eigen__2 ) )
=> ~ ( ~ sP26
=> ( X3 != X1 ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP1
=> ~ sP31 ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP1,
introduced(assumption,[]) ).
thf(h16,assumption,
sP31,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP17
| sP26
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP24
| sP26
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP20
| ~ sP26
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP21
| ~ sP26
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP11
| ~ sP1
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP37
| ~ sP1
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP15
| ~ sP1
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP9
| ~ sP1
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP19
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP13
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP14
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP33
| ~ sP30
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP3
| ~ sP30
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP25
| ~ sP30
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP12
| ~ sP30
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP36
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP28
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP35
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP32
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP2
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP29
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP23
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP34
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP27
| ~ sP5
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP6
| ~ sP8
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP18
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP10
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP38
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP31
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP31
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,h1,h3,h5,h7,h12,h15,h16]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,33,h15,h16]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,34,h14]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,35,h12,h13]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h10,36,h11]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h9,37,h10]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h8,38,h9]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,39,h7,h8]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,40,h5,h6]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,41,h3,h4]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,42,h1,h2]) ).
thf(0,theorem,
( sP4
=> ( sP18
=> ( sP10
=> ( sP38
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[43,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU704^2 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 20:56:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 22.60/22.82 % SZS status Theorem
% 22.60/22.82 % Mode: cade22grackle2x798d
% 22.60/22.82 % Steps: 35366
% 22.60/22.82 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------