TSTP Solution File: ALG270^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG270^5 : 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 : 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 : 600s
% DateTime : Thu Jul 14 17:57:53 EDT 2022
% Result : Theorem 1.91s 2.12s
% Output : Proof 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 44
% Syntax : Number of formulae : 52 ( 11 unt; 6 typ; 4 def)
% Number of atoms : 95 ( 26 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 311 ( 26 ~; 19 |; 0 &; 239 @)
% ( 18 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 24 con; 0-2 aty)
% Number of variables : 37 ( 4 ^ 33 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_c_star,type,
c_star: a > a > a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a] :
( ( c_star @ ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ X1 )
!= ( c_star @ eigen__0 @ ( c_star @ eigen__1 @ ( c_star @ eigen__2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a,X3: a] :
( ( c_star @ ( c_star @ ( c_star @ eigen__0 @ X1 ) @ X2 ) @ X3 )
= ( c_star @ eigen__0 @ ( c_star @ X1 @ ( c_star @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a,X3: a,X4: a] :
( ( c_star @ ( c_star @ ( c_star @ X1 @ X2 ) @ X3 ) @ X4 )
= ( c_star @ X1 @ ( c_star @ X2 @ ( c_star @ X3 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( c_star @ ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ X1 ) @ X2 )
= ( c_star @ eigen__0 @ ( c_star @ eigen__1 @ ( c_star @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a,X3: a] :
( ( c_star @ ( c_star @ X1 @ X2 ) @ X3 )
= ( c_star @ X1 @ ( c_star @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( c_star @ ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ eigen__3 )
= ( c_star @ eigen__0 @ ( c_star @ eigen__1 @ ( c_star @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( c_star @ ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ eigen__3 )
= ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ ( c_star @ eigen__2 @ eigen__3 ) ) )
=> ( ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ ( c_star @ eigen__2 @ eigen__3 ) )
!= ( c_star @ eigen__0 @ ( c_star @ eigen__1 @ ( c_star @ eigen__2 @ eigen__3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ X1 )
= ( c_star @ eigen__0 @ ( c_star @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a,X2: a] :
( ( c_star @ ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ X1 ) @ X2 )
= ( c_star @ eigen__0 @ ( c_star @ eigen__1 @ ( c_star @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ ( c_star @ eigen__2 @ eigen__3 ) )
= ( c_star @ eigen__0 @ ( c_star @ eigen__1 @ ( c_star @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ( ( c_star @ ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ eigen__3 )
= X1 )
=> ( X1
!= ( c_star @ eigen__0 @ ( c_star @ eigen__1 @ ( c_star @ eigen__2 @ eigen__3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP2
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a,X2: a] :
( ( c_star @ ( c_star @ eigen__0 @ X1 ) @ X2 )
= ( c_star @ eigen__0 @ ( c_star @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ( c_star @ ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ X1 )
= ( c_star @ eigen__0 @ ( c_star @ eigen__1 @ ( c_star @ eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a,X2: a > $o] :
( ( X2 @ X1 )
=> ! [X3: a] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a,X2: a] :
( ( c_star @ ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ X1 ) @ X2 )
= ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ ( c_star @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a,X2: a,X3: a,X4: a] :
( ( c_star @ ( c_star @ ( c_star @ X1 @ X2 ) @ X3 ) @ X4 )
= ( c_star @ X1 @ ( c_star @ X2 @ ( c_star @ X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP1
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( c_star @ ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ eigen__3 )
= ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ ( c_star @ eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a,X2: a,X3: a] :
( ( c_star @ ( c_star @ ( c_star @ eigen__0 @ X1 ) @ X2 ) @ X3 )
= ( c_star @ eigen__0 @ ( c_star @ X1 @ ( c_star @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > $o] :
( ( X1 @ ( c_star @ ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ eigen__3 ) )
=> ! [X2: a] :
( ( ( c_star @ ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ eigen__3 )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a] :
( ( c_star @ ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ X1 )
= ( c_star @ ( c_star @ eigen__0 @ eigen__1 ) @ ( c_star @ eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(cTHM23_pme,conjecture,
sP14 ).
thf(h1,negated_conjecture,
~ sP14,
inference(assume_negation,[status(cth)],[cTHM23_pme]) ).
thf(1,plain,
( ~ sP4
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP1
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP12
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP18
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| ~ sP15
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP7
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| sP2
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP17
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP1
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP9
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
sP11,
inference(eq_ind,[status(thm)],]) ).
thf(13,plain,
( sP10
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(14,plain,
( sP5
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(15,plain,
( sP16
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(16,plain,
( sP13
| ~ sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(17,plain,
( sP14
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP14
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h1]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[19,h0]) ).
thf(0,theorem,
sP14,
inference(contra,[status(thm),contra(discharge,[h1])],[19,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ALG270^5 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.10 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Thu Jun 9 00:35:37 EDT 2022
% 0.10/0.29 % CPUTime :
% 1.91/2.12 % SZS status Theorem
% 1.91/2.12 % Mode: mode506
% 1.91/2.12 % Inferences: 9
% 1.91/2.12 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------