TSTP Solution File: ALG290^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ALG290^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n032.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 : Wed Aug 30 16:33:53 EDT 2023
% Result : Theorem 0.14s 0.54s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 75
% Syntax : Number of formulae : 94 ( 34 unt; 12 typ; 2 def)
% Number of atoms : 254 ( 87 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 981 ( 271 ~; 24 |; 0 &; 433 @)
% ( 20 <=>; 233 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 27 con; 0-2 aty)
% Number of variables : 195 ( 10 ^; 185 !; 0 ?; 195 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cP,type,
cP: a > a > a ).
thf(ty_cF,type,
cF: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_cR,type,
cR: a > a ).
thf(ty_eigen__13,type,
eigen__13: a ).
thf(ty_cL,type,
cL: a > a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_cG,type,
cG: a > $o ).
thf(ty_eigen__14,type,
eigen__14: a ).
thf(ty_cZ,type,
cZ: a ).
thf(ty_cX,type,
cX: a > $o ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__0
@ ^ [X1: a] :
~ ( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
=> ( cX @ X2 ) )
=> ~ ( cG @ ( cP @ X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__0
@ ^ [X1: a] :
~ ( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
=> ( cX @ X2 ) )
=> ~ ( cF @ ( cP @ X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
=> ( cX @ X2 ) )
=> ~ ( cF @ ( cP @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
=> ( cX @ X2 ) )
=> ~ ( ~ ( cF @ ( cP @ X1 @ eigen__0 ) )
=> ( cG @ ( cP @ X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__13 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) )
=> ~ ( cF @ ( cP @ eigen__13 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__13 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) )
=> ~ ( ~ ( cF @ ( cP @ eigen__13 @ eigen__0 ) )
=> ( cG @ ( cP @ eigen__13 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cF @ ( cP @ eigen__13 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__13 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP5
=> ( cG @ ( cP @ eigen__13 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__14 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) )
=> ~ ( cG @ ( cP @ eigen__14 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP1
=> ~ ! [X1: a] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
=> ( cX @ X2 ) )
=> ~ ( cG @ ( cP @ X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cF @ ( cP @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( cF @ ( cP @ eigen__14 @ eigen__0 ) )
=> ( cG @ ( cP @ eigen__14 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) )
=> ~ ( cG @ ( cP @ eigen__1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP10
=> ( cG @ ( cP @ eigen__1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
=> ( cX @ X2 ) )
=> ~ ( cG @ ( cP @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__14 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cG @ ( cP @ eigen__14 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( cG @ ( cP @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP15
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
=> ( cX @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP19
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(cPU_X2310A_pme,conjecture,
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) )
=> ( ( ^ [X1: a] :
~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( ~ ( cF @ ( cP @ X2 @ X1 ) )
=> ( cG @ ( cP @ X2 @ X1 ) ) ) ) )
= ( ^ [X1: a] :
( ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cF @ ( cP @ X2 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cG @ ( cP @ X2 @ X1 ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) )
=> ( ( ^ [X1: a] :
~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( ~ ( cF @ ( cP @ X2 @ X1 ) )
=> ( cG @ ( cP @ X2 @ X1 ) ) ) ) )
= ( ^ [X1: a] :
( ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cF @ ( cP @ X2 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cG @ ( cP @ X2 @ X1 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cPU_X2310A_pme]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ( ^ [X1: a] :
~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( ~ ( cF @ ( cP @ X2 @ X1 ) )
=> ( cG @ ( cP @ X2 @ X1 ) ) ) ) )
!= ( ^ [X1: a] :
( ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cF @ ( cP @ X2 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cG @ ( cP @ X2 @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ),
introduced(assumption,[]) ).
thf(h12,assumption,
( ( cL @ cZ )
= cZ ),
introduced(assumption,[]) ).
thf(h13,assumption,
( ( cR @ cZ )
= cZ ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: a] :
( ( ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( ~ ( cF @ ( cP @ X2 @ X1 ) )
=> ( cG @ ( cP @ X2 @ X1 ) ) ) ) )
= ( ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cF @ ( cP @ X2 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cG @ ( cP @ X2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
( ~ sP2 != sP9 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h17,assumption,
sP9,
introduced(assumption,[]) ).
thf(h18,assumption,
sP2,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP19
=> ~ sP13 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP19,
introduced(assumption,[]) ).
thf(h22,assumption,
sP13,
introduced(assumption,[]) ).
thf(h23,assumption,
sP1,
introduced(assumption,[]) ).
thf(h24,assumption,
sP14,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP12
| ~ sP19
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP20
| ~ sP19
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP14
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP13
| sP10
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h24,h21,h22,h20,h16,h17,h15,h14,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,h21,h22,h23,h24]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h20,h16,h17,h15,h14,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h23,h24])],[h17,6,h23,h24]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h16,h17,h15,h14,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,7,h21,h22]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h15,h14,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__1)],[h16,8,h20]) ).
thf(10,plain,
( sP11
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP18
| ~ sP15
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP2
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP7
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP4
| ~ sP6
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( sP8
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP8
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP3
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP3
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP14
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14]) ).
thf(21,plain,
( sP1
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).
thf(22,plain,
( ~ sP9
| ~ sP1
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h19,h15,h14,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[10,11,12,13,14,15,16,17,18,19,20,21,22,h18,h19]) ).
thf(24,plain,
$false,
inference(tab_be,[status(thm),assumptions([h15,h14,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_be(discharge,[h16,h17]),tab_be(discharge,[h18,h19])],[h15,9,23,h16,h17,h18,h19]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__0)],[h14,24,h15]) ).
thf(26,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_fe(discharge,[h14])],[h3,25,h14]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,26,h12,h13]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,27,h10,h11]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,28,h8,h9]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,29,h6,h7]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,30,h4,h5]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,31,h2,h3]) ).
thf(33,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[32,h0]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) )
=> ( ( ^ [X1: a] :
~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( ~ ( cF @ ( cP @ X2 @ X1 ) )
=> ( cG @ ( cP @ X2 @ X1 ) ) ) ) )
= ( ^ [X1: a] :
( ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cF @ ( cP @ X2 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
=> ( cX @ X3 ) )
=> ~ ( cG @ ( cP @ X2 @ X1 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[32,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ALG290^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.29 % Computer : n032.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Mon Aug 28 05:41:00 EDT 2023
% 0.12/0.29 % CPUTime :
% 0.14/0.54 % SZS status Theorem
% 0.14/0.54 % Mode: cade22grackle2xfee4
% 0.14/0.54 % Steps: 7237
% 0.14/0.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------