TSTP Solution File: ITP072^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP072^1 : TPTP v8.1.2. Released v7.5.0.
% 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 04:01:53 EDT 2023
% Result : Theorem 0.18s 0.52s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 50
% Syntax : Number of formulae : 58 ( 17 unt; 6 typ; 1 def)
% Number of atoms : 125 ( 23 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 116 ( 30 ~; 23 |; 0 &; 46 @)
% ( 16 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 22 con; 0-2 aty)
% Number of variables : 20 ( 9 ^; 11 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_hF_Mirabelle_hf,type,
hF_Mirabelle_hf: $tType ).
thf(ty_eigen__0,type,
eigen__0: hF_Mirabelle_hf ).
thf(ty_eigen__8,type,
eigen__8: hF_Mirabelle_hf ).
thf(ty_hF_Mirabelle_hmem,type,
hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
thf(ty_z,type,
z: hF_Mirabelle_hf ).
thf(ty_zero_z189798548lle_hf,type,
zero_z189798548lle_hf: hF_Mirabelle_hf ).
thf(h0,assumption,
! [X1: hF_Mirabelle_hf > $o,X2: hF_Mirabelle_hf] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf )
!= ( hF_Mirabelle_hmem @ X1 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ^ [X1: hF_Mirabelle_hf] : ( zero_z189798548lle_hf = X1 ) )
= ( ^ [X1: hF_Mirabelle_hf] :
! [X2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X2 @ zero_z189798548lle_hf )
= ( hF_Mirabelle_hmem @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf )
= ( hF_Mirabelle_hmem @ X1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X1 @ z ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( hF_Mirabelle_hmem @ eigen__8 @ zero_z189798548lle_hf )
= ( hF_Mirabelle_hmem @ eigen__8 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = X1 )
= ( ! [X2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X2 @ zero_z189798548lle_hf )
= ( hF_Mirabelle_hmem @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( hF_Mirabelle_hmem @ eigen__0 @ zero_z189798548lle_hf ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( zero_z189798548lle_hf = z ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP8 = sP3 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( hF_Mirabelle_hmem @ eigen__8 @ z ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( z = zero_z189798548lle_hf ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP7
= ( hF_Mirabelle_hmem @ eigen__0 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( hF_Mirabelle_hmem @ eigen__0 @ z ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( ^ [X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] : ( X1 = X2 ) )
= ( ^ [X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
! [X3: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X3 @ X1 )
= ( hF_Mirabelle_hmem @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( hF_Mirabelle_hmem @ eigen__8 @ zero_z189798548lle_hf ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: hF_Mirabelle_hf] :
( ( ^ [X2: hF_Mirabelle_hf] : ( X1 = X2 ) )
= ( ^ [X2: hF_Mirabelle_hf] :
! [X3: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X3 @ X1 )
= ( hF_Mirabelle_hmem @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(conj_0,conjecture,
sP11 = sP4 ).
thf(h1,negated_conjecture,
sP11 != sP4,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h2,assumption,
sP11,
introduced(assumption,[]) ).
thf(h3,assumption,
sP4,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h6,assumption,
sP13,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP12
| sP7
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| ~ sP8
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| ~ sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP2
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP16
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP14
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| sP8 ),
inference(symeq,[status(thm)],]) ).
thf(fact_1_hemptyE,axiom,
sP1 ).
thf(fact_0_hf__ext,axiom,
sP14 ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,h2,h6,fact_1_hemptyE,fact_0_hf__ext]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h3,10,h6]) ).
thf(12,plain,
( ~ sP1
| ~ sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP4
| ~ sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( sP5
| sP15
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP3
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(16,plain,
( ~ sP9
| sP8
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP6
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP2
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP16
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP14
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP8
| sP11 ),
inference(symeq,[status(thm)],]) ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h1,h0])],[12,13,14,15,16,17,18,19,20,21,h4,h5,fact_1_hemptyE,fact_0_hf__ext]) ).
thf(23,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,11,22,h2,h3,h4,h5]) ).
thf(24,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[23,h0]) ).
thf(0,theorem,
sP11 = sP4,
inference(contra,[status(thm),contra(discharge,[h1])],[23,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP072^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 15:58:04 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.52 % SZS status Theorem
% 0.18/0.52 % Mode: cade22sinegrackle2x6978
% 0.18/0.52 % Steps: 1818
% 0.18/0.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------