TSTP Solution File: ITP094^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP094^1 : 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 : n013.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 04:02:00 EDT 2023
% Result : Theorem 20.27s 20.48s
% Output : Proof 20.27s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_real,type,
real: $tType ).
thf(ty_set_real,type,
set_real: $tType ).
thf(ty_poly_real,type,
poly_real: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_coeff_real,type,
coeff_real: poly_real > nat > real ).
thf(ty_zero_zero_real,type,
zero_zero_real: real ).
thf(ty_zero_zero_poly_real,type,
zero_zero_poly_real: poly_real ).
thf(ty_poly_real2,type,
poly_real2: poly_real > real > real ).
thf(ty_collect_real,type,
collect_real: ( real > $o ) > set_real ).
thf(ty_x,type,
x: real ).
thf(ty_finite_finite_real,type,
finite_finite_real: set_real > $o ).
thf(ty_ring_1_Ints_real,type,
ring_1_Ints_real: set_real ).
thf(ty_member_real,type,
member_real: real > set_real > $o ).
thf(ty_eigen__0,type,
eigen__0: poly_real ).
thf(ty_pderiv_real,type,
pderiv_real: poly_real > poly_real ).
thf(ty_p,type,
p: poly_real ).
thf(sP1,plain,
( sP1
<=> ! [X1: poly_real] :
( ( X1 != zero_zero_poly_real )
=> ( finite_finite_real
@ ( collect_real
@ ^ [X2: real] :
( ( poly_real2 @ X1 @ X2 )
= zero_zero_real ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( finite_finite_real
@ ( collect_real
@ ^ [X1: real] :
( ( poly_real2 @ ( pderiv_real @ p ) @ X1 )
= zero_zero_real ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( pderiv_real @ p )
!= zero_zero_poly_real )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( pderiv_real @ p )
= zero_zero_poly_real ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(conj_0,conjecture,
sP2 ).
thf(h0,negated_conjecture,
~ sP2,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ ( ! [X1: nat] : ( member_real @ ( coeff_real @ eigen__0 @ X1 ) @ ring_1_Ints_real )
=> ( ( eigen__0 != zero_zero_poly_real )
=> ( ( poly_real2 @ eigen__0 @ x )
!= zero_zero_real ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
! [X1: nat] : ( member_real @ ( coeff_real @ eigen__0 @ X1 ) @ ring_1_Ints_real ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ( eigen__0 != zero_zero_poly_real )
=> ( ( poly_real2 @ eigen__0 @ x )
!= zero_zero_real ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
eigen__0 != zero_zero_poly_real,
introduced(assumption,[]) ).
thf(h5,assumption,
( ( poly_real2 @ eigen__0 @ x )
= zero_zero_real ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP4
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_4__092_060open_062pderiv_Ap_A_092_060noteq_062_A0_092_060close_062,axiom,
~ sP4 ).
thf(fact_2_poly__roots__finite,axiom,
sP1 ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h2,h3,h1,h0])],[1,2,h0,fact_4__092_060open_062pderiv_Ap_A_092_060noteq_062_A0_092_060close_062,fact_2_poly__roots__finite]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,3,h4,h5]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,4,h2,h3]) ).
thf(fact_63__092_060open_062_092_060And_062thesisa_O_A_I_092_060And_062p_O_A_092_060lbrakk_062_092_060And_062i_O_Acoeff_Ap_Ai_A_092_060in_062_A_092_060int_062_059_Ap_A_092_060noteq_062_A0_059_Apoly_Ap_Ax_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesisa_J_A_092_060Longrightarrow_062_Athesisa_092_060close_062,axiom,
~ ! [X1: poly_real] :
( ! [X2: nat] : ( member_real @ ( coeff_real @ X1 @ X2 ) @ ring_1_Ints_real )
=> ( ( X1 != zero_zero_poly_real )
=> ( ( poly_real2 @ X1 @ x )
!= zero_zero_real ) ) ) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_63__092_060open_062_092_060And_062thesisa_O_A_I_092_060And_062p_O_A_092_060lbrakk_062_092_060And_062i_O_Acoeff_Ap_Ai_A_092_060in_062_A_092_060int_062_059_Ap_A_092_060noteq_062_A0_059_Apoly_Ap_Ax_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesisa_J_A_092_060Longrightarrow_062_Athesisa_092_060close_062,5,h1]) ).
thf(0,theorem,
sP2,
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP094^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n013.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 14:25:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 20.27/20.48 % SZS status Theorem
% 20.27/20.48 % Mode: cade22sinegrackle2xfaf3
% 20.27/20.48 % Steps: 177
% 20.27/20.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------