%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU653^2 : 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 : n012.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 02:33:12 PM UTC 2025
% Result : Theorem 133.00s 132.40s
% Output : Proof 133.00s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(sP1,plain,
( sP1
<=> ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__2 = eigen__3 )
=> ( eigen__1 = eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] : ( in @ X1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__2 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( in @ eigen__1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__0 @ emptyset ) ) )
=> ( ( eigen__1 != eigen__0 )
=> ( eigen__1 = eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( eigen__0 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X3 )
=> ( X1 = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP1
=> ( eigen__0 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( in @ eigen__1 @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( eigen__0 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) )
= ( setadjoin @ X1 @ emptyset ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( ( eigen__2 = X1 )
=> ( eigen__1 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( in @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) )
=> ( ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) )
!= ( setadjoin @ eigen__0 @ emptyset ) )
=> ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) )
= ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] : ( in @ X1 @ ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( in @ eigen__1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__0 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( setadjoin @ eigen__0 @ emptyset )
= ( setadjoin @ eigen__2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i,X2: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1 = X2 )
=> ( eigen__1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( in @ X1 @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) )
=> ( ( X1 != eigen__2 )
=> ( X1 = eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP15
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i,X2: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1 = X2 )
=> ( eigen__3 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( eigen__0 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( in @ eigen__1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP1
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( in @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X3 != X1 )
=> ( X3 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X2
!= ( setadjoin @ eigen__0 @ emptyset ) )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X2 != eigen__0 )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( ( eigen__0 = X1 )
=> ( eigen__3 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( in @ eigen__2 @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__2 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) )
= ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) )
=> ( ( eigen__0 = eigen__1 )
=> ( eigen__3 = eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( eigen__1 != eigen__2 )
=> ( eigen__1 = eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] : ( in @ X1 @ ( setadjoin @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i,X2: $i] :
( ( ( setadjoin @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i] :
( ( in @ X1 @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1
!= ( setadjoin @ eigen__0 @ emptyset ) )
=> ( X1
= ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: $i] :
( ( in @ X1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__0 @ emptyset ) ) )
=> ( ( X1 != eigen__0 )
=> ( X1 = eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ( eigen__0 = eigen__1 )
=> ( eigen__3 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( in @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) )
= ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) )
= ( setadjoin @ eigen__0 @ emptyset ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( eigen__1 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X3 )
=> ( X1 = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) )
!= ( setadjoin @ eigen__0 @ emptyset ) )
=> sP45 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( eigen__3 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__3 @ emptyset ) )
= ( setadjoin @ eigen__0 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X2 != eigen__2 )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__0 @ emptyset ) )
= ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__2 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X3 = X4 )
=> ( X2 = X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ( setadjoin @ eigen__2 @ ( setadjoin @ eigen__2 @ emptyset ) )
= ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__0 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP10
=> sP36 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> $false ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(def_secondinupair,definition,
secondinupair = sP3 ).
thf(def_upairset2E,definition,
( upairset2E
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
@ ( ( X3 = X1 )
| ( X3 = X2 ) ) ) ) ) ).
thf(def_setukpairinjL2,definition,
( setukpairinjL2
= ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
@ ( X1 = X3 ) ) ) ) ).
thf(def_setukpairinjR1,definition,
( setukpairinjR1
= ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X3 = X4 )
@ ( X2 = X4 ) ) ) ) ) ).
thf(def_upairequniteq,definition,
( upairequniteq
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
= ( setadjoin @ X3 @ emptyset ) )
@ ( X1 = X2 ) ) ) ) ).
thf(setukpairinjR2,conjecture,
( sP3
=> ( sP29
=> ( sP16
=> ( sP56
=> ( sP43
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X4 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP3
=> ( sP29
=> ( sP16
=> ( sP56
=> ( sP43
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X4 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[setukpairinjR2]) ).
thf(h1,assumption,
sP3,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP29
=> ( sP16
=> ( sP56
=> ( sP43
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP29,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP16
=> ( sP56
=> ( sP43
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP16,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP56
=> ( sP43
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP56,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP43
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X4 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP43,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X4 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X3 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: $i,X2: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( eigen__1 = X2 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i] :
( ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ eigen__2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( eigen__1 = X1 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP1
=> sP47 ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP1,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP47,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP44
| sP28
| ~ sP38
| sP60 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP49
| sP52
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP17
| ~ sP28
| sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP18
| sP44 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP40
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP30
| sP40 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP3
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP29
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP26
| sP10
| ~ sP34
| sP60 ),
inference(mating_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP33
| sP19
| ~ sP57
| ~ sP55 ),
inference(mating_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP35
| ~ sP38
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP32
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP24
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP48
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP45
| sP34 ),
inference(symeq,[status(thm)],[]) ).
thf(16,plain,
( sP54
| ~ sP20
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP54
| sP57 ),
inference(symeq,[status(thm)],[]) ).
thf(18,plain,
( ~ sP36
| sP59
| sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP58
| ~ sP10
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP20
| sP60
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP46
| ~ sP52
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP13
| sP46 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP22
| sP58 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP9
| ~ sP1
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP27
| ~ sP1
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP2
| ~ sP5
| sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP39
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP53
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP14
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP59
| sP55 ),
inference(symeq,[status(thm)],[]) ).
thf(32,plain,
( ~ sP37
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP3
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP43
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP29
| sP53 ),
inference(all_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP56
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP11
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP21
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP8
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP23
| sP15
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP6
| ~ sP19
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP41
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP42
| ~ sP51
| sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP25
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP31
| sP41 ),
inference(all_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP15
| sP51 ),
inference(symeq,[status(thm)],[]) ).
thf(47,plain,
( ~ sP4
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP16
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP29
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP56
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(52,plain,
~ sP60,
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP1
| sP38 ),
inference(symeq,[status(thm)],[]) ).
thf(54,plain,
( ~ sP50
| sP47 ),
inference(symeq,[status(thm)],[]) ).
thf(55,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h13,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,h1,h3,h5,h7,h9,h15,h16]) ).
thf(56,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h13,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,55,h15,h16]) ).
thf(57,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,56,h14]) ).
thf(58,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h12,57,h13]) ).
thf(59,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[h11,58,h12]) ).
thf(60,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__0)],[h10,59,h11]) ).
thf(61,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,60,h9,h10]) ).
thf(62,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,61,h7,h8]) ).
thf(63,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,62,h5,h6]) ).
thf(64,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,63,h3,h4]) ).
thf(65,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,64,h1,h2]) ).
thf(0,theorem,
( sP3
=> ( sP29
=> ( sP16
=> ( sP56
=> ( sP43
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X4 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[65,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU653^2 : TPTP v9.2.0. Released v3.7.0.
% 0.11/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n012.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
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 8 21:29:23 EDT 2025
% 0.14/0.34 % CPUTime :
% 133.00/132.40 % SZS status Theorem
% 133.00/132.40 % Mode: cade22grackle2xb9cd
% 133.00/132.40 % Steps: 125745
% 133.00/132.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------