TSTP Solution File: SEU781^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU781^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n003.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 14:05:01 EDT 2022
% Result : Theorem 0.36s 0.59s
% Output : Proof 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 82
% Syntax : Number of formulae : 100 ( 28 unt; 12 typ; 4 def)
% Number of atoms : 300 ( 4 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 940 ( 87 ~; 27 |; 0 &; 620 @)
% ( 26 <=>; 180 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 38 con; 0-3 aty)
% Number of variables : 108 ( 5 ^ 103 !; 0 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__16,type,
eigen__16: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cartprod,type,
cartprod: $i > $i > $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $o ).
thf(ty_kpair,type,
kpair: $i > $i > $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_breln1compset,type,
breln1compset: $i > $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__16,definition,
( eigen__16
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ( in @ X1 @ eigen__0 )
=> ~ ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X1 @ eigen__4 ) @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(sP1,plain,
( sP1
<=> ( ( subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ X1 ) )
=> ~ ! [X4: $i] :
( ~ ( ( in @ X4 @ eigen__0 )
=> ~ ( in @ ( kpair @ X2 @ X4 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X4 @ X3 ) @ X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X1 @ eigen__4 ) @ eigen__2 )
=> eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
=> ~ ! [X3: $i] :
( ~ ( ( in @ X3 @ eigen__0 )
=> ~ ( in @ ( kpair @ X1 @ X3 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X3 @ X2 ) @ eigen__2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ~ ( ( in @ X1 @ eigen__0 )
=> ~ ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X1 @ eigen__4 ) @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
=> ~ ! [X2: $i] :
( ~ ( ( in @ X2 @ eigen__0 )
=> ~ ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X2 @ X1 ) @ eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
=> ~ ! [X3: $i] :
( ~ ( ( in @ X3 @ eigen__0 )
=> ~ ( in @ ( kpair @ X1 @ X3 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X3 @ X2 ) @ eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( in @ ( kpair @ eigen__3 @ eigen__16 ) @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__16 @ eigen__4 ) @ eigen__2 )
=> eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( in @ eigen__16 @ eigen__0 )
=> ~ ( in @ ( kpair @ eigen__3 @ eigen__16 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( in @ ( kpair @ eigen__16 @ eigen__4 ) @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( in @ eigen__16 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
=> ~ ! [X2: $i] :
( ~ ( ( in @ X2 @ eigen__0 )
=> ~ ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X2 @ X1 ) @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( in @ eigen__4 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ eigen__4 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
=> ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ X1 ) )
=> ~ ! [X4: $i] :
( ~ ( ( in @ X4 @ eigen__0 )
=> ~ ( in @ ( kpair @ X2 @ X4 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X4 @ X3 ) @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP11
=> eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( in @ ( kpair @ eigen__3 @ eigen__16 ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i] :
( ( subset @ X2 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ eigen__0 @ X1 @ X2 ) )
=> ~ ! [X5: $i] :
( ~ ( ( in @ X5 @ eigen__0 )
=> ~ ( in @ ( kpair @ X3 @ X5 ) @ X1 ) )
=> ~ ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( in @ ( kpair @ eigen__3 @ eigen__4 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> eigen__5 ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X1 @ X2 @ X3 ) )
=> ~ ! [X6: $i] :
( ~ ( ( in @ X6 @ X1 )
=> ~ ( in @ ( kpair @ X4 @ X6 ) @ X2 ) )
=> ~ ( in @ ( kpair @ X6 @ X5 ) @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP12
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP10
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP20
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( in @ eigen__4 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(def_breln,definition,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).
thf(def_breln1,definition,
( breln1
= ( ^ [X1: $i] : ( breln @ X1 @ X1 ) ) ) ).
thf(def_breln1compE,definition,
( breln1compE
= ( ! [X1: $i,X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X1 @ X3 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X1 @ X2 @ X3 ) )
=> ~ ! [X6: $i] :
( ~ ( ( in @ X6 @ X1 )
=> ~ ( in @ ( kpair @ X4 @ X6 ) @ X2 ) )
=> ~ ( in @ ( kpair @ X6 @ X5 ) @ X3 ) ) ) ) ) ) ) ) ) ).
thf(breln1compEex,conjecture,
( sP22
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X1 @ X2 @ X3 ) )
=> ! [X6: $o] :
( ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X7 ) @ X2 )
=> ( ( in @ ( kpair @ X7 @ X5 ) @ X3 )
=> X6 ) ) )
=> X6 ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP22
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X1 @ X2 @ X3 ) )
=> ! [X6: $o] :
( ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X7 ) @ X2 )
=> ( ( in @ ( kpair @ X7 @ X5 ) @ X3 )
=> X6 ) ) )
=> X6 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[breln1compEex]) ).
thf(h2,assumption,
sP22,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X1 @ X2 @ X3 ) )
=> ! [X6: $o] :
( ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X7 ) @ X2 )
=> ( ( in @ ( kpair @ X7 @ X5 ) @ X3 )
=> X6 ) ) )
=> X6 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i] :
( ( subset @ X2 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ eigen__0 @ X1 @ X2 ) )
=> ! [X5: $o] :
( ! [X6: $i] :
( ( in @ X6 @ eigen__0 )
=> ( ( in @ ( kpair @ X3 @ X6 ) @ X1 )
=> ( ( in @ ( kpair @ X6 @ X4 ) @ X2 )
=> X5 ) ) )
=> X5 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP4
=> ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ X1 ) )
=> ! [X4: $o] :
( ! [X5: $i] :
( ( in @ X5 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X5 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X5 @ X3 ) @ X1 )
=> X4 ) ) )
=> X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP4,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ X1 ) )
=> ! [X4: $o] :
( ! [X5: $i] :
( ( in @ X5 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X5 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X5 @ X3 ) @ X1 )
=> X4 ) ) )
=> X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP13
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
=> ! [X3: $o] :
( ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ X4 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X4 @ X2 ) @ eigen__2 )
=> X3 ) ) )
=> X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP13,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
=> ! [X3: $o] :
( ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ X4 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X4 @ X2 ) @ eigen__2 )
=> X3 ) ) )
=> X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP7
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X3 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X3 @ X1 ) @ eigen__2 )
=> X2 ) ) )
=> X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP7,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 ) @ ( breln1compset @ eigen__0 @ eigen__1 @ eigen__2 ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X3 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X3 @ X1 ) @ eigen__2 )
=> X2 ) ) )
=> X2 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP26
=> ( sP20
=> ! [X1: $o] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X2 @ eigen__4 ) @ eigen__2 )
=> X1 ) ) )
=> X1 ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP26,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP20
=> ! [X1: $o] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X2 @ eigen__4 ) @ eigen__2 )
=> X1 ) ) )
=> X1 ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP20,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ! [X1: $o] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X2 @ eigen__4 ) @ eigen__2 )
=> X1 ) ) )
=> X1 ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP2
=> sP21 ),
introduced(assumption,[]) ).
thf(h20,assumption,
sP2,
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP21,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP23
| ~ sP12
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| ~ sP18
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP17
| ~ sP11
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP10
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP10
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP24
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP24
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP5
| ~ sP24 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__16]) ).
thf(10,plain,
( ~ sP14
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP15
| ~ sP26
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP25
| ~ sP20
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP8
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP6
| ~ sP7
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP16
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP3
| ~ sP13
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP22
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP19
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP1
| ~ sP4
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h20,h21,h19,h17,h18,h15,h16,h14,h12,h13,h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,h2,h6,h9,h12,h15,h17,h20,h21]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h17,h18,h15,h16,h14,h12,h13,h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,20,h20,h21]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h18,h15,h16,h14,h12,h13,h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__5)],[h18,21,h19]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,22,h17,h18]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,23,h15,h16]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__4)],[h13,24,h14]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,25,h12,h13]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__3)],[h10,26,h11]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,27,h9,h10]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[h7,28,h8]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,29,h6,h7]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,30,h5]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h3,31,h4]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,32,h2,h3]) ).
thf(34,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[33,h0]) ).
thf(0,theorem,
( sP22
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X1 @ X2 @ X3 ) )
=> ! [X6: $o] :
( ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X7 ) @ X2 )
=> ( ( in @ ( kpair @ X7 @ X5 ) @ X3 )
=> X6 ) ) )
=> X6 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[33,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU781^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n003.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 : Mon Jun 20 13:42:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.36/0.59 % SZS status Theorem
% 0.36/0.59 % Mode: mode213
% 0.36/0.59 % Inferences: 1413
% 0.36/0.59 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------