TSTP Solution File: ITP193^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP193^1 : 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 : n017.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 00:29:27 EDT 2022
% Result : Theorem 45.91s 46.06s
% Output : Proof 45.91s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set_real,type,
set_real: $tType ).
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_a,type,
a: real ).
thf(ty_zero_zero_real,type,
zero_zero_real: real ).
thf(ty_p,type,
p: poly_real ).
thf(ty_b,type,
b: real ).
thf(ty_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(ty_finite_finite_real,type,
finite_finite_real: set_real > $o ).
thf(ty_collect_real,type,
collect_real: ( real > $o ) > set_real ).
thf(sP1,plain,
( sP1
<=> ( finite_finite_real
@ ( collect_real
@ ^ [X1: real] :
( ( poly_real2 @ p @ X1 )
= zero_zero_real ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: real > $o] :
( ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [X2: real] :
~ ( ( ( poly_real2 @ p @ X2 )
= zero_zero_real )
=> ~ ( ord_less_real @ a @ X2 ) ) ) )
=> ( finite_finite_real @ ( collect_real @ X1 ) ) )
=> ( finite_finite_real
@ ( collect_real
@ ^ [X2: real] :
~ ( ~ ( ( ( poly_real2 @ p @ X2 )
= zero_zero_real )
=> ~ ( ord_less_real @ a @ X2 ) )
=> ~ ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: real > $o] :
( ( ~ sP1
=> ( finite_finite_real @ ( collect_real @ X1 ) ) )
=> ( finite_finite_real
@ ( collect_real
@ ^ [X2: real] :
~ ( ( ( poly_real2 @ p @ X2 )
= zero_zero_real )
=> ~ ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [X1: real] :
~ ( ( ( poly_real2 @ p @ X1 )
= zero_zero_real )
=> ~ ( ord_less_real @ a @ X1 ) ) ) )
=> ( finite_finite_real
@ ( collect_real
@ ^ [X1: real] : ( ord_less_real @ X1 @ b ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: real > $o,X2: real > $o] :
( ( ~ ( finite_finite_real @ ( collect_real @ X1 ) )
=> ( finite_finite_real @ ( collect_real @ X2 ) ) )
=> ( finite_finite_real
@ ( collect_real
@ ^ [X3: real] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ~ sP1
=> ( finite_finite_real @ ( collect_real @ ( ord_less_real @ a ) ) ) )
=> ( finite_finite_real
@ ( collect_real
@ ^ [X1: real] :
~ ( ( ( poly_real2 @ p @ X1 )
= zero_zero_real )
=> ~ ( ord_less_real @ a @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( finite_finite_real
@ ( collect_real
@ ^ [X1: real] :
~ ( ~ ( ( ( poly_real2 @ p @ X1 )
= zero_zero_real )
=> ~ ( ord_less_real @ a @ X1 ) )
=> ~ ( ord_less_real @ X1 @ b ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( finite_finite_real
@ ( collect_real
@ ^ [X1: real] :
~ ( ( ( poly_real2 @ p @ X1 )
= zero_zero_real )
=> ~ ( ord_less_real @ a @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP4
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP1
=> ( finite_finite_real @ ( collect_real @ ( ord_less_real @ a ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(conj_0,conjecture,
sP7 ).
thf(h0,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( sP10
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP4
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| ~ sP10
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP2
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP9
| ~ sP4
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(fact_11_finite__Collect__conjI,axiom,
sP5 ).
thf(fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062,axiom,
sP1 ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,fact_11_finite__Collect__conjI,fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062,h0]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP193^1 : 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
% 0.13/0.34 % Computer : n017.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 16:25:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 45.91/46.06 % SZS status Theorem
% 45.91/46.06 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 45.91/46.06 % Inferences: 73
% 45.91/46.06 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------