%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU909^5 : 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 : n013.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 02:52:56 PM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 40
% Syntax : Number of formulae : 60 ( 26 unt; 0 typ; 1 def)
% Number of atoms : 202 ( 15 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 749 ( 219 ~; 8 |; 0 &; 266 @)
% ( 10 <=>; 246 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 176 ( 29 ^; 147 !; 0 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__3,type,
eigen__3: a > $o ).
thf(ty_cA,type,
cA: ( a > $o ) > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( cA @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: ( a > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( eigen__1 @ X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ eigen__1 ) )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 )
=> ( eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( eigen__1 @ X1 )
=> ( eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ sP2
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cA @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: ( a > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( eigen__1 @ X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ( cA @ eigen__4 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 )
=> ( eigen__4 @ X1 ) ) )
=> ~ ( ( cA @ eigen__4 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 )
=> ( eigen__4 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( cA @ eigen__4 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a > $o] :
( ~ ( ! [X2: ( a > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( eigen__3 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( eigen__1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(cDOMTHM8_pme,conjecture,
~ ( ! [X1: a > $o] :
( ( cA @ X1 )
=> ( cA @ X1 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ! [X2: ( a > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a > $o] :
( ( cA @ X3 )
=> ~ ( X3 @ X2 ) ) ) )
=> ~ ( ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( cA @ X2 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : $false )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X1 @ X5 )
=> ( X4 @ X5 ) ) ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
( ! [X1: a > $o] :
( ( cA @ X1 )
=> ( cA @ X1 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ! [X2: ( a > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a > $o] :
( ( cA @ X3 )
=> ~ ( X3 @ X2 ) ) ) )
=> ~ ( ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( cA @ X2 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : $false )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X1 @ X5 )
=> ( X4 @ X5 ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cDOMTHM8_pme]) ).
thf(h2,assumption,
~ ! [X1: a > $o] :
( ( cA @ X1 )
=> ( cA @ X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a > $o] :
( ~ ( ! [X2: ( a > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a > $o] :
( ( cA @ X3 )
=> ~ ( X3 @ X2 ) ) ) )
=> ~ ( ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( cA @ X2 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : $false )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X1 @ X5 )
=> ( X4 @ X5 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP6
=> sP6 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP6,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h5,h6,h4,h2,h1,h0])],[h5,h6]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,1,h5,h6]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h2,2,h4]) ).
thf(h7,assumption,
~ ( ~ ( sP7
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: a > $o] :
( ( cA @ X2 )
=> ~ ( X2 @ X1 ) ) ) )
=> ~ ( ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) )
=> ( cA @ X1 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( eigen__1 @ X4 )
=> ( X3 @ X4 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP7
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: a > $o] :
( ( cA @ X2 )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
( ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) )
=> ( cA @ X1 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( eigen__1 @ X4 )
=> ( X3 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP7,
introduced(assumption,[]) ).
thf(h11,assumption,
! [X1: a] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: a > $o] :
( ( cA @ X2 )
=> ~ ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) )
=> ( cA @ X1 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( eigen__1 @ X4 )
=> ( X3 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ ( sP1
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> sP1 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP1
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h17,assumption,
sP1,
introduced(assumption,[]) ).
thf(h18,assumption,
! [X1: a] :
( ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ),
introduced(assumption,[]) ).
thf(4,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h18,h15,h16,h14,h12,h10,h11,h8,h9,h7,h3,h1,h0])],[h17,h16]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h12,h10,h11,h8,h9,h7,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,4,h17,h18]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h10,h11,h8,h9,h7,h3,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,5,h15,h16]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h10,h11,h8,h9,h7,h3,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__2)],[h12,6,h14]) ).
thf(h19,assumption,
~ ( ~ ( ( cA @ eigen__3 )
=> ~ sP3 )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( ( cA @ eigen__3 )
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP10,
introduced(assumption,[]) ).
thf(h22,assumption,
cA @ eigen__3,
introduced(assumption,[]) ).
thf(h23,assumption,
sP3,
introduced(assumption,[]) ).
thf(8,plain,
( sP8
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP8
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP4
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(11,plain,
( ~ sP10
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP5
| sP2
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP2
| ~ sP7
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h22,h23,h20,h21,h19,h13,h10,h11,h8,h9,h7,h3,h1,h0])],[8,9,10,11,12,13,h10,h23,h21]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h19,h13,h10,h11,h8,h9,h7,h3,h1,h0]),tab_negimp(discharge,[h22,h23])],[h20,14,h22,h23]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h13,h10,h11,h8,h9,h7,h3,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,15,h20,h21]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h10,h11,h8,h9,h7,h3,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__3)],[h13,16,h19]) ).
thf(18,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h11,h8,h9,h7,h3,h1,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h13])],[h9,7,17,h12,h13]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,18,h10,h11]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,19,h8,h9]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h3,20,h7]) ).
thf(22,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h2]),tab_imp(discharge,[h3])],[h1,3,21,h2,h3]) ).
thf(23,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[22,h0]) ).
thf(0,theorem,
~ ( ! [X1: a > $o] :
( ( cA @ X1 )
=> ( cA @ X1 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ! [X2: ( a > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a > $o] :
( ( cA @ X3 )
=> ~ ( X3 @ X2 ) ) ) )
=> ~ ( ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( cA @ X2 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : $false )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X1 @ X5 )
=> ( X4 @ X5 ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[22,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU909^5 : TPTP v9.2.0. Released v4.0.0.
% 0.10/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 20:35:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % Mode: mode213
% 0.12/0.37 % Inferences: 14
% 0.12/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------