TSTP Solution File: SEU861^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU861^5 : 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 : n010.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 Aug 31 17:37:41 EDT 2023
% Result : Theorem 1.30s 1.50s
% Output : Proof 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 49
% Syntax : Number of formulae : 59 ( 15 unt; 6 typ; 1 def)
% Number of atoms : 135 ( 14 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 265 ( 83 ~; 19 |; 0 &; 72 @)
% ( 18 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 22 con; 0-2 aty)
% Number of variables : 54 ( 1 ^; 53 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cB,type,
cB: a > $o ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_cC,type,
cC: a > $o ).
thf(ty_eigen__26,type,
eigen__26: a ).
thf(ty_eigen__0,type,
eigen__0: ( a > $o ) > $o ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__26,definition,
( eigen__26
= ( eps__0
@ ^ [X1: a] :
~ ( ( cB @ X1 )
=> ( ~ ( cC @ X1 )
=> ( X1 = eigen__5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__26])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > $o,X2: a,X3: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ~ ( X1 @ X4 )
=> ( X4 = X2 ) ) ) )
=> ( eigen__0 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: a > $o] :
( ! [X2: a] :
~ ( X1 @ X2 )
=> ( eigen__0 @ X1 ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0 @ cC )
=> ~ ! [X1: a] :
( ( cB @ X1 )
=> ( ~ ( cC @ X1 )
=> ( X1 = eigen__5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: ( a > $o ) > $o] :
( ~ ( ! [X2: a > $o] :
( ! [X3: a] :
~ ( X2 @ X3 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a > $o,X3: a,X4: a > $o] :
( ~ ( ( X1 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ~ ( X2 @ X5 )
=> ( X5 = X3 ) ) ) )
=> ( X1 @ X4 ) ) )
=> ( X1 @ cC ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cB @ eigen__26 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a,X2: a > $o] :
( ~ ( ( eigen__0 @ cC )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ~ ( cC @ X3 )
=> ( X3 = X1 ) ) ) )
=> ( eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP5
=> ( ~ ( cC @ eigen__26 )
=> ( eigen__26 = eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP5
=> ( cC @ eigen__26 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP2
=> ( eigen__0 @ cC ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cC @ eigen__26 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP3
=> ( eigen__0 @ cB ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a > $o] :
( ! [X2: a] :
~ ( X1 @ X2 )
=> ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__0 @ cB ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ cC )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( ~ ( cC @ X2 )
=> ( X2 = eigen__5 ) ) ) )
=> ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0 @ cC ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP10
=> ( eigen__26 = eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a] :
( ( cB @ X1 )
=> ( cC @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a] :
( ( cB @ X1 )
=> ( ~ ( cC @ X1 )
=> ( X1 = eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(cTHM531E_pme,conjecture,
( ~ ( sP4
=> ~ sP17 )
=> ! [X1: ( a > $o ) > $o] :
( ~ ( ! [X2: a > $o] :
( ! [X3: a] :
~ ( X2 @ X3 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a > $o,X3: a,X4: a > $o] :
( ~ ( ( X1 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ~ ( X2 @ X5 )
=> ( X5 = X3 ) ) ) )
=> ( X1 @ X4 ) ) )
=> ( X1 @ cB ) ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( sP4
=> ~ sP17 )
=> ! [X1: ( a > $o ) > $o] :
( ~ ( ! [X2: a > $o] :
( ! [X3: a] :
~ ( X2 @ X3 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a > $o,X3: a,X4: a > $o] :
( ~ ( ( X1 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ~ ( X2 @ X5 )
=> ( X5 = X3 ) ) ) )
=> ( X1 @ X4 ) ) )
=> ( X1 @ cB ) ) ),
inference(assume_negation,[status(cth)],[cTHM531E_pme]) ).
thf(h2,assumption,
~ ( sP4
=> ~ sP17 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: ( a > $o ) > $o] :
( ~ ( ! [X2: a > $o] :
( ! [X3: a] :
~ ( X2 @ X3 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a > $o,X3: a,X4: a > $o] :
( ~ ( ( X1 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ~ ( X2 @ X5 )
=> ( X5 = X3 ) ) ) )
=> ( X1 @ X4 ) ) )
=> ( X1 @ cB ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP4,
introduced(assumption,[]) ).
thf(h5,assumption,
sP17,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ sP2
=> sP13 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h9,assumption,
sP12,
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| ~ sP5
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP17
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP16
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP7
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP7
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP18
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__26]) ).
thf(7,plain,
( ~ sP3
| ~ sP15
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP11
| sP3
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP14
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP2
| ~ sP12
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP9
| sP2
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP4
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h7,h8,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h4,h5,h9,h10,h8]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,15,h9,h10]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,16,h7,h8]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h3,17,h6]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,18,h4,h5]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,19,h2,h3]) ).
thf(21,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[20,h0]) ).
thf(0,theorem,
( ~ ( sP4
=> ~ sP17 )
=> ! [X1: ( a > $o ) > $o] :
( ~ ( ! [X2: a > $o] :
( ! [X3: a] :
~ ( X2 @ X3 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a > $o,X3: a,X4: a > $o] :
( ~ ( ( X1 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ~ ( X2 @ X5 )
=> ( X5 = X3 ) ) ) )
=> ( X1 @ X4 ) ) )
=> ( X1 @ cB ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[20,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU861^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n010.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 Aug 23 18:44:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 1.30/1.50 % SZS status Theorem
% 1.30/1.50 % Mode: cade22grackle2xfee4
% 1.30/1.50 % Steps: 35631
% 1.30/1.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------