%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV008^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 02:56:06 PM UTC 2025
% Result : Theorem 38.69s 38.89s
% Output : Proof 38.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 102
% Syntax : Number of formulae : 133 ( 53 unt; 0 typ; 2 def)
% Number of atoms : 299 ( 19 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 976 ( 410 ~; 38 |; 0 &; 261 @)
% ( 37 <=>; 230 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 50 usr; 45 con; 0-2 aty)
% Number of variables : 143 ( 2 ^; 141 !; 0 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__14,type,
eigen__14: a > $o ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__12,type,
eigen__12: a ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__24,type,
eigen__24: a > $o ).
thf(ty_eigen__15,type,
eigen__15: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__0,type,
eigen__0: ( a > $o ) > $o ).
thf(ty_eigen__11,type,
eigen__11: a ).
thf(ty_eigen__8,type,
eigen__8: a > $o ).
thf(ty_eigen__13,type,
eigen__13: a ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__1 ) )
=> ( X2 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__24,definition,
( eigen__24
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__12 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__12 ) )
=> ( X2 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__24])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 ) )
=> ( X3 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ( eigen__0 @ eigen__2 )
=> ~ ( eigen__2 @ eigen__1 ) )
=> ~ ( eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__8 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__14 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ( eigen__0 @ eigen__24 )
=> ~ ( eigen__24 @ eigen__12 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__12 ) )
=> ( X1 = eigen__24 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__14 = eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__15 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__24 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__1 ) )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ( eigen__0 @ eigen__14 )
=> ~ ( eigen__14 @ eigen__11 ) )
=> ~ ( eigen__14 @ eigen__13 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP12
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__12 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__12 ) )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__7 ) )
=> ~ ( X1 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP8
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__12 ) )
=> ( X1 = eigen__24 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( eigen__0 @ eigen__14 )
=> ~ ( eigen__14 @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__14 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP16
=> ~ ( eigen__8 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a] :
( ( eigen__15 @ X1 )
= ( eigen__24 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( eigen__14 @ eigen__13 )
= sP9 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__15 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ ( ( eigen__0 @ eigen__2 )
=> ~ ( eigen__2 @ eigen__1 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ( X1 = eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__0 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__8 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a] :
( ( eigen__14 @ X1 )
= ( eigen__24 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP25
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__15 = eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP23 = sP9 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP29
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( eigen__14 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( eigen__0 @ eigen__2 )
=> ~ ( eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__11 ) )
=> ~ ( X1 @ eigen__13 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ sP13
=> sP30 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(cTHM261_pme,conjecture,
! [X1: ( a > $o ) > $o] :
( ~ ( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: a] :
~ ! [X3: a > $o] :
( ~ ( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ( X4 = X3 ) ) ) )
=> ~ ( ~ ( ! [X2: a] :
~ ! [X3: a > $o] :
( ~ ( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ~ ( X4 @ X3 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) )
=> ~ ( X4 @ X2 ) ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ~ ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X2 ) )
=> ~ ( X5 @ X3 ) )
=> ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X3 ) )
=> ~ ( X5 @ X4 ) ) )
=> ~ ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X2 ) )
=> ~ ( X5 @ X4 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: ( a > $o ) > $o] :
( ~ ( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: a] :
~ ! [X3: a > $o] :
( ~ ( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ( X4 = X3 ) ) ) )
=> ~ ( ~ ( ! [X2: a] :
~ ! [X3: a > $o] :
( ~ ( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ~ ( X4 @ X3 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) )
=> ~ ( X4 @ X2 ) ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ~ ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X2 ) )
=> ~ ( X5 @ X3 ) )
=> ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X3 ) )
=> ~ ( X5 @ X4 ) ) )
=> ~ ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X2 ) )
=> ~ ( X5 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM261_pme]) ).
thf(h2,assumption,
~ ( ~ ( ! [X1: a > $o] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) )
=> ~ sP1 )
=> ~ ( ~ ( ! [X1: a] :
~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ( X2 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 ) )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ( X3 @ X1 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ~ ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X1 ) )
=> ~ ( X4 @ X2 ) )
=> ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ~ ( X4 @ X3 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X1 ) )
=> ~ ( X4 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ! [X1: a > $o] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ~ ( ! [X1: a] :
~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ( X2 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 ) )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ( X3 @ X1 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ~ ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X1 ) )
=> ~ ( X4 @ X2 ) )
=> ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ~ ( X4 @ X3 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X1 ) )
=> ~ ( X4 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: a > $o] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
( ! [X1: a] :
~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ( X2 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 ) )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ( X3 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ~ ( ~ ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X1 ) )
=> ~ ( X4 @ X2 ) )
=> ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ~ ( X4 @ X3 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X1 ) )
=> ~ ( X4 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: a] :
~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ( X2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: a,X2: a] :
( ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 ) )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ( X3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP27,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP34
| ~ sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP27
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( sP34
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP24
| ~ sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP10
| ~ sP24 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(6,plain,
( ~ sP1
| ~ sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,h6,h11]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__1)],[h9,7,h11]) ).
thf(h12,assumption,
~ ! [X1: a] :
( ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__6 ) )
=> ~ ( X2 @ X1 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ( X2 @ eigen__6 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__6 ) )
=> ~ ( X1 @ eigen__7 ) )
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__6 ) )
=> ~ ( X1 @ eigen__7 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP15,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( ~ ( sP8
=> ~ sP26 )
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP8
=> ~ sP26 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP3,
introduced(assumption,[]) ).
thf(h19,assumption,
sP8,
introduced(assumption,[]) ).
thf(h20,assumption,
sP26,
introduced(assumption,[]) ).
thf(9,plain,
( ~ sP16
| ~ sP8
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP20
| sP16
| ~ sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP15
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h20,h17,h18,h16,h14,h15,h13,h12,h10,h7,h5,h6,h3,h4,h2,h1,h0])],[9,10,11,h19,h20,h18,h15]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h16,h14,h15,h13,h12,h10,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,12,h19,h20]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h13,h12,h10,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,13,h17,h18]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h13,h12,h10,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__8)],[h14,14,h16]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h12,h10,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,15,h14,h15]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h10,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__7)],[h12,16,h13]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__6)],[h10,17,h12]) ).
thf(19,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h5,h6,h3,h4,h2,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h7,8,18,h9,h10]) ).
thf(h21,assumption,
~ ! [X1: a,X2: a] :
( ~ ( ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ eigen__11 ) )
=> ~ ( X3 @ X1 ) )
=> ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 ) )
=> ~ ( X3 @ X2 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ eigen__11 ) )
=> ~ ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
~ ! [X1: a] :
( ~ ( ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__11 ) )
=> ~ ( X2 @ eigen__12 ) )
=> ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__12 ) )
=> ~ ( X2 @ X1 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__11 ) )
=> ~ ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( ~ ( ~ ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__11 ) )
=> ~ ( X1 @ eigen__12 ) )
=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__12 ) )
=> ~ ( X1 @ eigen__13 ) ) )
=> ~ sP35 ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( ~ ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__11 ) )
=> ~ ( X1 @ eigen__12 ) )
=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__12 ) )
=> ~ ( X1 @ eigen__13 ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
sP35,
introduced(assumption,[]) ).
thf(h26,assumption,
~ ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__11 ) )
=> ~ ( X1 @ eigen__12 ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__12 ) )
=> ~ ( X1 @ eigen__13 ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
~ ( ~ sP18
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h29,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h30,assumption,
sP4,
introduced(assumption,[]) ).
thf(h31,assumption,
sP25,
introduced(assumption,[]) ).
thf(h32,assumption,
sP19,
introduced(assumption,[]) ).
thf(h33,assumption,
~ ( ~ sP13
=> ~ sP23 ),
introduced(assumption,[]) ).
thf(h34,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h35,assumption,
sP23,
introduced(assumption,[]) ).
thf(h36,assumption,
sP12,
introduced(assumption,[]) ).
thf(h37,assumption,
sP7,
introduced(assumption,[]) ).
thf(20,plain,
( ~ sP22
| sP33
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP31
| ~ sP23
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP28
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP6
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP21
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP30
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP29
| ~ sP25
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP32
| sP29
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP13
| ~ sP12
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP36
| sP13
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP17
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP17
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(32,plain,
( sP5
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( sP14
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__24]) ).
thf(34,plain,
( ~ sP18
| ~ sP25
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP11
| sP18
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP1
| ~ sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP35
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h36,h37,h34,h35,h33,h31,h32,h29,h30,h28,h26,h27,h24,h25,h23,h22,h21,h8,h5,h6,h3,h4,h2,h1,h0])],[20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,h6,h31,h32,h30,h36,h37,h35,h25]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h34,h35,h33,h31,h32,h29,h30,h28,h26,h27,h24,h25,h23,h22,h21,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h36,h37])],[h34,38,h36,h37]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h31,h32,h29,h30,h28,h26,h27,h24,h25,h23,h22,h21,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h34,h35])],[h33,39,h34,h35]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h31,h32,h29,h30,h28,h26,h27,h24,h25,h23,h22,h21,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h33]),tab_negall(eigenvar,eigen__15)],[h27,40,h33]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h30,h28,h26,h27,h24,h25,h23,h22,h21,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h29,41,h31,h32]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h26,h27,h24,h25,h23,h22,h21,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h28,42,h29,h30]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h26,h27,h24,h25,h23,h22,h21,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__14)],[h26,43,h28]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h25,h23,h22,h21,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h26,h27])],[h24,44,h26,h27]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h22,h21,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,45,h24,h25]) ).
thf(47,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h22,h21,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__13)],[h22,46,h23]) ).
thf(48,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h22]),tab_negall(eigenvar,eigen__12)],[h21,47,h22]) ).
thf(49,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__11)],[h8,48,h21]) ).
thf(50,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h4,19,49,h7,h8]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,50,h5,h6]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,51,h3,h4]) ).
thf(53,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,52,h2]) ).
thf(54,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[53,h0]) ).
thf(0,theorem,
! [X1: ( a > $o ) > $o] :
( ~ ( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: a] :
~ ! [X3: a > $o] :
( ~ ( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ( X4 = X3 ) ) ) )
=> ~ ( ~ ( ! [X2: a] :
~ ! [X3: a > $o] :
( ~ ( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ~ ( X4 @ X3 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) )
=> ~ ( X4 @ X2 ) ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ~ ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X2 ) )
=> ~ ( X5 @ X3 ) )
=> ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X3 ) )
=> ~ ( X5 @ X4 ) ) )
=> ~ ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X2 ) )
=> ~ ( X5 @ X4 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[53,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV008^5 : TPTP v9.2.0. Released v4.0.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 19:02:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 38.69/38.89 % SZS status Theorem
% 38.69/38.89 % Mode: mode484
% 38.69/38.89 % Inferences: 916
% 38.69/38.89 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------