TSTP Solution File: ITP113^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP113^1 : 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 : n002.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 04:02:10 EDT 2023
% Result : Theorem 63.02s 61.92s
% Output : Proof 63.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 65
% Syntax : Number of formulae : 76 ( 23 unt; 25 typ; 2 def)
% Number of atoms : 96 ( 9 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 202 ( 37 ~; 17 |; 0 &; 122 @)
% ( 15 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 36 usr; 29 con; 0-2 aty)
% Number of variables : 18 ( 2 ^; 16 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_extended_ereal,type,
extended_ereal: $tType ).
thf(ty_product_prod_a_real,type,
product_prod_a_real: $tType ).
thf(ty_set_a,type,
set_a: $tType ).
thf(ty_real,type,
real: $tType ).
thf(ty_set_Pr1928503567a_real,type,
set_Pr1928503567a_real: $tType ).
thf(ty_ord_less_eq_real,type,
ord_less_eq_real: real > real > $o ).
thf(ty_thesis,type,
thesis: $o ).
thf(ty_e,type,
e: real ).
thf(ty_lower_930854854raph_a,type,
lower_930854854raph_a: set_a > ( a > extended_ereal ) > set_Pr1928503567a_real ).
thf(ty_eigen__0,type,
eigen__0: product_prod_a_real ).
thf(ty_y,type,
y: real ).
thf(ty_top_top_set_a,type,
top_top_set_a: set_a ).
thf(ty_member1103263856a_real,type,
member1103263856a_real: product_prod_a_real > set_Pr1928503567a_real > $o ).
thf(ty_top_to2138011583a_real,type,
top_to2138011583a_real: set_Pr1928503567a_real ).
thf(ty_eigen__6,type,
eigen__6: real ).
thf(ty_z,type,
z: real ).
thf(ty_elemen1695521870a_real,type,
elemen1695521870a_real: set_Pr1928503567a_real > set_Pr1928503567a_real ).
thf(ty_eigen__1,type,
eigen__1: product_prod_a_real ).
thf(ty_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(ty_f,type,
f: a > extended_ereal ).
thf(ty_product_Pair_a_real,type,
product_Pair_a_real: a > real > product_prod_a_real ).
thf(ty_x,type,
x: a ).
thf(ty_real_V404783528a_real,type,
real_V404783528a_real: product_prod_a_real > product_prod_a_real > real ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(h0,assumption,
! [X1: real > $o,X2: real] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: real] :
( eigen__1
!= ( product_Pair_a_real @ eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: real] :
( eigen__1
!= ( product_Pair_a_real @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( member1103263856a_real @ eigen__1 @ ( lower_930854854raph_a @ top_top_set_a @ f ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a,X2: real] :
( eigen__1
!= ( product_Pair_a_real @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: real] :
( ~ ( ( member1103263856a_real @ ( product_Pair_a_real @ eigen__5 @ X1 ) @ ( lower_930854854raph_a @ top_top_set_a @ f ) )
=> ~ ( ord_less_real @ ( real_V404783528a_real @ ( product_Pair_a_real @ eigen__5 @ X1 ) @ ( product_Pair_a_real @ x @ y ) ) @ e ) )
=> thesis ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> thesis ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( member1103263856a_real @ ( product_Pair_a_real @ eigen__5 @ eigen__6 ) @ ( lower_930854854raph_a @ top_top_set_a @ f ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: real] :
( eigen__1
!= ( product_Pair_a_real @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: product_prod_a_real] :
~ ! [X2: a,X3: real] :
( X1
!= ( product_Pair_a_real @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP6
=> ~ ( ord_less_real @ ( real_V404783528a_real @ ( product_Pair_a_real @ eigen__5 @ eigen__6 ) @ ( product_Pair_a_real @ x @ y ) ) @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a,X2: real] :
( ~ ( ( member1103263856a_real @ ( product_Pair_a_real @ X1 @ X2 ) @ ( lower_930854854raph_a @ top_top_set_a @ f ) )
=> ~ ( ord_less_real @ ( real_V404783528a_real @ ( product_Pair_a_real @ X1 @ X2 ) @ ( product_Pair_a_real @ x @ y ) ) @ e ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( real_V404783528a_real @ eigen__1 @ ( product_Pair_a_real @ x @ y ) )
= ( real_V404783528a_real @ ( product_Pair_a_real @ eigen__5 @ eigen__6 ) @ ( product_Pair_a_real @ x @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ord_less_real @ ( real_V404783528a_real @ eigen__1 @ ( product_Pair_a_real @ x @ y ) ) @ e ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__1
= ( product_Pair_a_real @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP9
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ord_less_real @ ( real_V404783528a_real @ ( product_Pair_a_real @ eigen__5 @ eigen__6 ) @ ( product_Pair_a_real @ x @ y ) ) @ e ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(conj_1,conjecture,
sP5 ).
thf(h2,negated_conjecture,
~ sP5,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(h3,assumption,
member1103263856a_real @ eigen__0 @ top_to2138011583a_real,
introduced(assumption,[]) ).
thf(h4,assumption,
member1103263856a_real @ ( product_Pair_a_real @ x @ y ) @ ( elemen1695521870a_real @ ( lower_930854854raph_a @ top_top_set_a @ f ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
ord_less_eq_real @ y @ z,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP1
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
sP12,
introduced(assumption,[]) ).
thf(1,plain,
( sP11
| sP3
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP12
| sP15
| sP3
| ~ sP11 ),
inference(mating_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP1
| sP6
| sP3
| ~ sP13 ),
inference(mating_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| ~ sP6
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP14
| sP9
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP10
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( sP7
| sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(9,plain,
( sP2
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).
thf(10,plain,
( ~ sP8
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
~ sP3,
inference(prop_rule,[status(thm)],]) ).
thf(conj_0,axiom,
sP10 ).
thf(fact_280_old_Oprod_Oexhaust,axiom,
sP8 ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h2,conj_0,fact_280_old_Oprod_Oexhaust,h7,h8]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,12,h7,h8]) ).
thf(fact_0__092_060open_062_092_060exists_062ya_092_060in_062Epigraph_AUNIV_Af_O_Adist_Aya_A_Ix_M_Ay_J_A_060_Ae_092_060close_062,axiom,
~ ! [X1: product_prod_a_real] :
( ( member1103263856a_real @ X1 @ ( lower_930854854raph_a @ top_top_set_a @ f ) )
=> ~ ( ord_less_real @ ( real_V404783528a_real @ X1 @ ( product_Pair_a_real @ x @ y ) ) @ e ) ) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[fact_0__092_060open_062_092_060exists_062ya_092_060in_062Epigraph_AUNIV_Af_O_Adist_Aya_A_Ix_M_Ay_J_A_060_Ae_092_060close_062,13,h6]) ).
thf(fact_2_xy,axiom,
~ ( ( member1103263856a_real @ ( product_Pair_a_real @ x @ y ) @ ( elemen1695521870a_real @ ( lower_930854854raph_a @ top_top_set_a @ f ) ) )
=> ~ ( ord_less_eq_real @ y @ z ) ) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[fact_2_xy,14,h4,h5]) ).
thf(fact_290_UNIV__witness,axiom,
~ ! [X1: product_prod_a_real] :
~ ( member1103263856a_real @ X1 @ top_to2138011583a_real ) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[fact_290_UNIV__witness,15,h3]) ).
thf(17,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[16,h1]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[17,h0]) ).
thf(0,theorem,
sP5,
inference(contra,[status(thm),contra(discharge,[h2])],[16,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : ITP113^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 12:41:19 EDT 2023
% 0.14/0.35 % CPUTime :
% 63.02/61.92 % SZS status Theorem
% 63.02/61.92 % Mode: cade22sinegrackle2x78f3
% 63.02/61.92 % Steps: 9733
% 63.02/61.92 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------