TSTP Solution File: ITP056^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP056^1 : 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 : n032.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 00:28:55 EDT 2022
% Result : Theorem 1.34s 1.60s
% Output : Proof 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 151 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 120 ( 16 ~; 9 |; 0 &; 91 @)
% ( 0 <=>; 2 =>; 2 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 20 con; 0-2 aty)
% Number of variables : 4 ( 0 ^ 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(conj_0,conjecture,
( ( last_c571238084t_unit @ ( fe @ n ) )
= ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) ) ).
thf(h0,negated_conjecture,
( last_c571238084t_unit @ ( fe @ n ) )
!= ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(nax52,axiom,
( p52
<= ( ( flast_c571238084t_unit @ ( ffe @ fn ) )
= ( fnth_co1649820636t_unit @ ( ffe @ fn ) @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ ( ffe @ fn ) ) @ fone_one_nat ) ) ) ),
file('<stdin>',nax52) ).
thf(ax0,axiom,
~ p52,
file('<stdin>',ax0) ).
thf(pax2,axiom,
( p2
=> ! [X14: list_c1059388851t_unit] :
( ( X14 != fnil_co1338500125t_unit )
=> ( ( flast_c571238084t_unit @ X14 )
= ( fnth_co1649820636t_unit @ X14 @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ X14 ) @ fone_one_nat ) ) ) ) ),
file('<stdin>',pax2) ).
thf(nax1,axiom,
( p1
<= ( ( ffe @ fn )
= fnil_co1338500125t_unit ) ),
file('<stdin>',nax1) ).
thf(ax51,axiom,
~ p1,
file('<stdin>',ax51) ).
thf(ax50,axiom,
p2,
file('<stdin>',ax50) ).
thf(c_0_6,plain,
( ( ( flast_c571238084t_unit @ ( ffe @ fn ) )
!= ( fnth_co1649820636t_unit @ ( ffe @ fn ) @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ ( ffe @ fn ) ) @ fone_one_nat ) ) )
| p52 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax52])]) ).
thf(c_0_7,plain,
~ p52,
inference(fof_simplification,[status(thm)],[ax0]) ).
thf(c_0_8,plain,
! [X169: list_c1059388851t_unit] :
( ~ p2
| ( X169 = fnil_co1338500125t_unit )
| ( ( flast_c571238084t_unit @ X169 )
= ( fnth_co1649820636t_unit @ X169 @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ X169 ) @ fone_one_nat ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax2])])])]) ).
thf(c_0_9,plain,
( ( ( ffe @ fn )
!= fnil_co1338500125t_unit )
| p1 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])]) ).
thf(c_0_10,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax51]) ).
thf(c_0_11,plain,
( p52
| ( ( flast_c571238084t_unit @ ( ffe @ fn ) )
!= ( fnth_co1649820636t_unit @ ( ffe @ fn ) @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ ( ffe @ fn ) ) @ fone_one_nat ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_12,plain,
~ p52,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_13,plain,
! [X6: list_c1059388851t_unit] :
( ( X6 = fnil_co1338500125t_unit )
| ( ( flast_c571238084t_unit @ X6 )
= ( fnth_co1649820636t_unit @ X6 @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ X6 ) @ fone_one_nat ) ) )
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,plain,
p2,
inference(split_conjunct,[status(thm)],[ax50]) ).
thf(c_0_15,plain,
( p1
| ( ( ffe @ fn )
!= fnil_co1338500125t_unit ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_16,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_17,plain,
( fnth_co1649820636t_unit @ ( ffe @ fn ) @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ ( ffe @ fn ) ) @ fone_one_nat ) )
!= ( flast_c571238084t_unit @ ( ffe @ fn ) ),
inference(sr,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_18,plain,
! [X6: list_c1059388851t_unit] :
( ( ( fnth_co1649820636t_unit @ X6 @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ X6 ) @ fone_one_nat ) )
= ( flast_c571238084t_unit @ X6 ) )
| ( X6 = fnil_co1338500125t_unit ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
thf(c_0_19,plain,
( ffe @ fn )
!= fnil_co1338500125t_unit,
inference(sr,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( ( last_c571238084t_unit @ ( fe @ n ) )
= ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : ITP056^1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.10 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Thu Jun 2 14:07:45 EDT 2022
% 0.09/0.29 % CPUTime :
% 1.34/1.60 % SZS status Theorem
% 1.34/1.60 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 1.34/1.60 % Inferences: 1
% 1.34/1.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------