TSTP Solution File: SEV238^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV238^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 : 600s
% DateTime : Tue Jul 19 18:05:30 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 73
% Syntax : Number of formulae : 103 ( 49 unt; 8 typ; 1 def)
% Number of atoms : 216 ( 8 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 846 ( 197 ~; 18 |; 0 &; 410 @)
% ( 20 <=>; 201 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 84 ( 84 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 28 con; 0-2 aty)
% Number of variables : 223 ( 49 ^ 174 !; 0 ?; 223 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__2 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__2 @ eigen__5 )
=> ~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__0 @ eigen__2 @ X1 ) )
=> ~ ( eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( eigen__0 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__0 @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0 @ eigen__2 @ eigen__1 )
=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) )
=> ! [X1: $i] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP5
=> ( eigen__0 @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP8
=> ( eigen__0
@ ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) )
@ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0 @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__0
@ ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) )
@ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(cTHM2D_pme,conjecture,
! [X1: ( $i > $o ) > $i > $o] :
( ~ ( ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) )
@ X3 ) ) )
=> ~ ( ! [X2: $i] :
( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
=> ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ( X1
@ ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
@ X2 ) ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ( ! [X3: $i] :
( ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) )
@ X3 )
=> ( X1
@ ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) ) )
@ X3 ) )
=> ~ ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: ( $i > $o ) > $i > $o] :
( ~ ( ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) )
@ X3 ) ) )
=> ~ ( ! [X2: $i] :
( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
=> ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ( X1
@ ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
@ X2 ) ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ( ! [X3: $i] :
( ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) )
@ X3 )
=> ( X1
@ ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) ) )
@ X3 ) )
=> ~ ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM2D_pme]) ).
thf(h2,assumption,
~ ( ~ ( sP3
=> ~ ( ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) )
=> sP17 ) )
=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ( sP17
=> ~ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP3
=> ~ ( ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) )
=> sP17 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ( sP17
=> ~ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP3,
introduced(assumption,[]) ).
thf(h6,assumption,
( ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) )
=> sP17 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP17,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__1 ) )
=> sP18 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP6
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP6,
introduced(assumption,[]) ).
thf(h14,assumption,
sP5,
introduced(assumption,[]) ).
thf(h15,assumption,
sP14
!= ( ~ ( sP17
=> ~ sP14 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP14,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP17
=> ~ sP14 ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h19,assumption,
( sP17
=> ~ sP14 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__4 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) )
@ eigen__4 ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__4 ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( eigen__0
@ ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) )
@ eigen__4 ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP11
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP6
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP1
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP1
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP13
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(6,plain,
( ~ sP3
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP9
| ~ sP13
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP20
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP7
| ~ sP15
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| ~ sP5
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h22,h23,h21,h20,h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h5,h13,h14,h11]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h20,h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,12,h22,h23]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h20,h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__4)],[h20,13,h21]) ).
thf(15,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h18,h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[h16,h18]) ).
thf(16,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_imp(discharge,[h20]),tab_imp(discharge,[h18])],[h17,14,15,h20,h18]) ).
thf(17,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h8,h16,h18,h19,h15,h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[h16,h18]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h19,h15,h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h16])],[h19,17,h8,h16]) ).
thf(19,plain,
$false,
inference(tab_be,[status(thm),assumptions([h15,h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_be(discharge,[h16,h17]),tab_be(discharge,[h18,h19])],[h15,16,18,h16,h17,h18,h19]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__3)],[h4,19,h15]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,20,h13,h14]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__2)],[h10,21,h12]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,22,h10,h11]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h7,23,h9]) ).
thf(h24,assumption,
sP4
!= ( ~ ( sP17
=> ~ sP4 ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
sP4,
introduced(assumption,[]) ).
thf(h26,assumption,
~ ( sP17
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h28,assumption,
( sP17
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h29,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h30,assumption,
sP8,
introduced(assumption,[]) ).
thf(h31,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(25,plain,
( ~ sP17
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP12
| ~ sP8
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h30,h31,h29,h20,h25,h26,h24,h8,h5,h6,h3,h4,h2,h1,h0])],[25,26,h8,h30,h31]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h20,h25,h26,h24,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h30,h31])],[h29,27,h30,h31]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h20,h25,h26,h24,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h29]),tab_negall(eigenvar,eigen__7)],[h20,28,h29]) ).
thf(30,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h27,h25,h26,h24,h8,h5,h6,h3,h4,h2,h1,h0])],[h25,h27]) ).
thf(31,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h25,h26,h24,h8,h5,h6,h3,h4,h2,h1,h0]),tab_imp(discharge,[h20]),tab_imp(discharge,[h27])],[h26,29,30,h20,h27]) ).
thf(32,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h8,h25,h27,h28,h24,h8,h5,h6,h3,h4,h2,h1,h0])],[h25,h27]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h28,h24,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h25])],[h28,32,h8,h25]) ).
thf(34,plain,
$false,
inference(tab_be,[status(thm),assumptions([h24,h8,h5,h6,h3,h4,h2,h1,h0]),tab_be(discharge,[h25,h26]),tab_be(discharge,[h27,h28])],[h24,31,33,h25,h26,h27,h28]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__6)],[h4,34,h24]) ).
thf(36,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,24,35,h7,h8]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,36,h5,h6]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,37,h3,h4]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,38,h2]) ).
thf(40,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[39,h0]) ).
thf(0,theorem,
! [X1: ( $i > $o ) > $i > $o] :
( ~ ( ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) )
@ X3 ) ) )
=> ~ ( ! [X2: $i] :
( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
=> ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ( X1
@ ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
@ X2 ) ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ( ! [X3: $i] :
( ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) )
@ X3 )
=> ( X1
@ ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) ) )
@ X3 ) )
=> ~ ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[39,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV238^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 28 15:36:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % Mode: mode213
% 0.12/0.37 % Inferences: 27
% 0.12/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------