TSTP Solution File: ITP195^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP195^1 : 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 : n027.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 00:29:28 EDT 2022
% Result : Theorem 2.37s 2.55s
% Output : Proof 2.37s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_poly_real,type,
poly_real: $tType ).
thf(ty_real,type,
real: $tType ).
thf(ty_poly_real2,type,
poly_real2: poly_real > real > real ).
thf(ty_zero_zero_real,type,
zero_zero_real: real ).
thf(ty_p,type,
p: poly_real ).
thf(ty_sturm_469514713_r_pos,type,
sturm_469514713_r_pos: poly_real > real > $o ).
thf(ty_pderiv_real,type,
pderiv_real: poly_real > poly_real ).
thf(ty_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(ty_x,type,
x: real ).
thf(sP1,plain,
( sP1
<=> ( sturm_469514713_r_pos @ p @ x ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( poly_real2 @ p @ x )
= zero_zero_real ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(conj_0,conjecture,
sP1
!= ( ( sP3
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
=> ~ ( ~ sP3
=> sP2 ) ) ).
thf(h0,negated_conjecture,
( sP1
= ( ( sP3
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
=> ~ ( ~ sP3
=> sP2 ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
( ( sP3
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
=> ~ ( ~ sP3
=> sP2 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( sP3
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
=> ~ ( ~ sP3
=> sP2 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP3
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ sP3
=> sP2 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP3,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h10,assumption,
sP2,
introduced(assumption,[]) ).
thf(fact_0_False,axiom,
~ sP3 ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h9,h7,h8,h5,h1,h2,h0])],[h7,fact_0_False]) ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h9,h7,h8,h5,h1,h2,h0])],[h10,h9]) ).
thf(fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,axiom,
( sP1
=> sP2 ) ).
thf(3,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h7,h8,h5,h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,1,2,h3,h10]) ).
thf(4,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h1,h7,h8,h5,h1,h2,h0])],[h1,h3]) ).
thf(5,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h1,h7,h8,h5,h1,h2,h0])],[h7,fact_0_False]) ).
thf(6,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h7,h8,h5,h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,4,5,h3,h10]) ).
thf(fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062,axiom,
( sP2
=> sP1 ) ).
thf(7,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h8,h5,h1,h2,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h1])],[fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062,3,6,h9,h1]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,7,h7,h8]) ).
thf(h11,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(9,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h9,h11,h9,h6,h1,h2,h0])],[h1,h3]) ).
thf(10,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h9,h11,h9,h6,h1,h2,h0])],[h10,h9]) ).
thf(11,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h11,h9,h6,h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,9,10,h3,h10]) ).
thf(12,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h1,h11,h9,h6,h1,h2,h0])],[h1,h3]) ).
thf(13,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h1,h11,h9,h6,h1,h2,h0])],[h10,h9]) ).
thf(14,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h11,h9,h6,h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,12,13,h3,h10]) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h11,h9,h6,h1,h2,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h1])],[fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062,11,14,h9,h1]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h1,h2,h0]),tab_negimp(discharge,[h11,h9])],[h6,15,h11,h9]) ).
thf(17,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h2,8,16,h5,h6]) ).
thf(h12,assumption,
( sP3
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
( ~ sP3
=> sP2 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x,
introduced(assumption,[]) ).
thf(18,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h9,h7,h11,h12,h13,h3,h4,h0])],[h7,h11]) ).
thf(19,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h9,h7,h11,h12,h13,h3,h4,h0])],[h10,h9]) ).
thf(20,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h7,h11,h12,h13,h3,h4,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,18,19,h3,h10]) ).
thf(21,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h1,h7,h11,h12,h13,h3,h4,h0])],[h1,h3]) ).
thf(22,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h1,h7,h11,h12,h13,h3,h4,h0])],[h7,h11]) ).
thf(23,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h7,h11,h12,h13,h3,h4,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,21,22,h3,h10]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h11,h12,h13,h3,h4,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h1])],[fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062,20,23,h9,h1]) ).
thf(25,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h9,h10,h11,h12,h13,h3,h4,h0])],[h10,h9]) ).
thf(26,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h9,h10,h11,h12,h13,h3,h4,h0])],[h10,h9]) ).
thf(27,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h10,h11,h12,h13,h3,h4,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,25,26,h3,h10]) ).
thf(28,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h1,h10,h11,h12,h13,h3,h4,h0])],[h1,h3]) ).
thf(29,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h1,h10,h11,h12,h13,h3,h4,h0])],[h1,h3]) ).
thf(30,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h10,h11,h12,h13,h3,h4,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,28,29,h3,h10]) ).
thf(31,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h11,h12,h13,h3,h4,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h1])],[fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062,27,30,h9,h1]) ).
thf(32,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h11,h12,h13,h3,h4,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h10])],[h13,24,31,h7,h10]) ).
thf(33,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h9,h7,h14,h12,h13,h3,h4,h0])],[h7,fact_0_False]) ).
thf(34,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h9,h7,h14,h12,h13,h3,h4,h0])],[h10,h9]) ).
thf(35,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h7,h14,h12,h13,h3,h4,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,33,34,h3,h10]) ).
thf(36,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h1,h7,h14,h12,h13,h3,h4,h0])],[h1,h3]) ).
thf(37,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h1,h7,h14,h12,h13,h3,h4,h0])],[h7,fact_0_False]) ).
thf(38,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h7,h14,h12,h13,h3,h4,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,36,37,h3,h10]) ).
thf(39,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h14,h12,h13,h3,h4,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h1])],[fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062,35,38,h9,h1]) ).
thf(40,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h9,h10,h14,h12,h13,h3,h4,h0])],[h10,h9]) ).
thf(41,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h9,h10,h14,h12,h13,h3,h4,h0])],[h10,h9]) ).
thf(42,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h10,h14,h12,h13,h3,h4,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,40,41,h3,h10]) ).
thf(43,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h1,h10,h14,h12,h13,h3,h4,h0])],[h1,h3]) ).
thf(44,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h1,h10,h14,h12,h13,h3,h4,h0])],[h1,h3]) ).
thf(45,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h10,h14,h12,h13,h3,h4,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,43,44,h3,h10]) ).
thf(46,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h14,h12,h13,h3,h4,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h1])],[fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062,42,45,h9,h1]) ).
thf(47,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h14,h12,h13,h3,h4,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h10])],[h13,39,46,h7,h10]) ).
thf(48,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h12,h13,h3,h4,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h14])],[h12,32,47,h11,h14]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h0]),tab_negimp(discharge,[h12,h13])],[h4,48,h12,h13]) ).
thf(50,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h0]),tab_bq(discharge,[h1,h2]),tab_bq(discharge,[h3,h4])],[h0,17,49,h1,h2,h3,h4]) ).
thf(0,theorem,
sP1
!= ( ( sP3
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
=> ~ ( ~ sP3
=> sP2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[50,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP195^1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n027.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 : 600
% 0.14/0.35 % DateTime : Fri Jun 3 02:07:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 2.37/2.55 % SZS status Theorem
% 2.37/2.55 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 2.37/2.55 % Inferences: 0
% 2.37/2.55 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------