TSTP Solution File: ITP072^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP072^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n021.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 : Sun Jul 17 00:28:59 EDT 2022
% Result : Theorem 47.69s 47.76s
% Output : Proof 47.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 49
% Syntax : Number of formulae : 55 ( 12 unt; 6 typ; 2 def)
% Number of atoms : 128 ( 28 equ; 3 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 125 ( 28 ~; 24 |; 0 &; 49 @)
% ( 20 <=>; 4 =>; 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 : 29 ( 26 usr; 27 con; 0-2 aty)
% Number of variables : 21 ( 6 ^ 15 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_hF_Mirabelle_hf,type,
hF_Mirabelle_hf: $tType ).
thf(ty_eigen__2,type,
eigen__2: hF_Mirabelle_hf ).
thf(ty_z,type,
z: hF_Mirabelle_hf ).
thf(ty_eigen__0,type,
eigen__0: hF_Mirabelle_hf ).
thf(ty_hF_Mirabelle_hmem,type,
hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
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__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: hF_Mirabelle_hf] :
~ ~ ( hF_Mirabelle_hmem @ X1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf )
!= ( hF_Mirabelle_hmem @ X1 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( (=)
= ( ^ [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,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X1 @ z ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: hF_Mirabelle_hf] :
( ( (=) @ X1 )
= ( ^ [X2: hF_Mirabelle_hf] :
! [X3: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X3 @ X1 )
= ( hF_Mirabelle_hmem @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( hF_Mirabelle_hmem @ eigen__2 @ zero_z189798548lle_hf ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( zero_z189798548lle_hf = z ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP6
= ( ! [X1: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf )
= ( hF_Mirabelle_hmem @ X1 @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( (=) @ zero_z189798548lle_hf )
= ( ^ [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,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP6
=> ( z = zero_z189798548lle_hf ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( z = zero_z189798548lle_hf ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( hF_Mirabelle_hmem @ eigen__0 @ z ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf )
= ( hF_Mirabelle_hmem @ X1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = X1 )
=> ( X1 = zero_z189798548lle_hf ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP10 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [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,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( hF_Mirabelle_hmem @ eigen__2 @ z ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( hF_Mirabelle_hmem @ eigen__0 @ zero_z189798548lle_hf ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP4 = sP18 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(conj_0,conjecture,
sP15 ).
thf(h1,negated_conjecture,
~ sP15,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP14
| ~ sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP14
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP19
| ~ sP5
| ~ sP10 ),
inference(mating_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| ~ sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP20
| sP4
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
sP5,
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP12
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(8,plain,
( ~ sP7
| sP6
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP17
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP8
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP3
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP1
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP2
| sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(14,plain,
( ~ sP9
| ~ sP6
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP13
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP16
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
sP16,
inference(eq_sym,[status(thm)],]) ).
thf(18,plain,
( sP15
| ~ sP10
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP15
| sP10
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(fact_1_hemptyE,axiom,
sP14 ).
thf(fact_0_hf__ext,axiom,
sP1 ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,fact_1_hemptyE,fact_0_hf__ext,h1]) ).
thf(21,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[20,h0]) ).
thf(0,theorem,
sP15,
inference(contra,[status(thm),contra(discharge,[h1])],[20,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP072^1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n021.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 : 600
% 0.13/0.34 % DateTime : Fri Jun 3 21:42:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 47.69/47.76 % SZS status Theorem
% 47.69/47.76 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 47.69/47.76 % Inferences: 5144
% 47.69/47.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------