TSTP Solution File: ITP012^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP012^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n001.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 04:01:03 EDT 2023
% Result : Theorem 1.46s 1.66s
% Output : Proof 1.46s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mono_2Etyop_2Einteger_2Eint,type,
mono_2Etyop_2Einteger_2Eint: $tType ).
thf(ty_eigen__2,type,
eigen__2: mono_2Etyop_2Einteger_2Eint ).
thf(ty_mono_2Ec_2Einteger_2Eint__add,type,
mono_2Ec_2Einteger_2Eint__add: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(ty_mono_2Ec_2Einteger_2Eint__sub,type,
mono_2Ec_2Einteger_2Eint__sub: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(ty_eigen__1,type,
eigen__1: mono_2Etyop_2Einteger_2Eint ).
thf(ty_eigen__0,type,
eigen__0: mono_2Etyop_2Einteger_2Eint ).
thf(ty_mono_2Ec_2Einteger_2Eint__divides,type,
mono_2Ec_2Einteger_2Eint__divides: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(ty_mono_2Ec_2Einteger_2Eint__neg,type,
mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(sP1,plain,
( sP1
<=> ! [X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint,X3: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2 )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ ( mono_2Ec_2Einteger_2Eint__add @ X3 @ X2 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: mono_2Etyop_2Einteger_2Eint] :
~ ( ( ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ ( mono_2Ec_2Einteger_2Eint__neg @ X1 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ X1 ) )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ eigen__0 ) @ X1 )
!= ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ ( mono_2Ec_2Einteger_2Eint__neg @ eigen__1 ) )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ ( mono_2Ec_2Einteger_2Eint__add @ X1 @ ( mono_2Ec_2Einteger_2Eint__neg @ eigen__1 ) ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( mono_2Ec_2Einteger_2Eint__sub @ eigen__2 @ eigen__1 )
= ( mono_2Ec_2Einteger_2Eint__add @ eigen__2 @ ( mono_2Ec_2Einteger_2Eint__neg @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ ( mono_2Ec_2Einteger_2Eint__sub @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ ( mono_2Ec_2Einteger_2Eint__neg @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
~ ( ( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ ( mono_2Ec_2Einteger_2Eint__neg @ X2 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2 ) )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ X1 ) @ X2 )
!= ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP6 = sP7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ X1 @ X2 )
= ( mono_2Ec_2Einteger_2Eint__add @ X1 @ ( mono_2Ec_2Einteger_2Eint__neg @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP9
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ eigen__0 ) @ eigen__1 )
!= sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ X1 )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ ( mono_2Ec_2Einteger_2Eint__add @ X2 @ X1 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ ( mono_2Ec_2Einteger_2Eint__add @ eigen__2 @ ( mono_2Ec_2Einteger_2Eint__neg @ eigen__1 ) ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( mono_2Ec_2Einteger_2Eint__add @ eigen__2 @ ( mono_2Ec_2Einteger_2Eint__neg @ eigen__1 ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP6
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ eigen__2 @ X1 )
= ( mono_2Ec_2Einteger_2Eint__add @ eigen__2 @ ( mono_2Ec_2Einteger_2Eint__neg @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> $false ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ ( mono_2Ec_2Einteger_2Eint__add @ eigen__2 @ ( mono_2Ec_2Einteger_2Eint__neg @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(thm_2Einteger_2EINT__DIVIDES__RSUB,conjecture,
! [X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint,X3: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2 )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ ( mono_2Ec_2Einteger_2Eint__sub @ X3 @ X2 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X3 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint,X3: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2 )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ ( mono_2Ec_2Einteger_2Eint__sub @ X3 @ X2 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X3 ) ) ),
inference(assume_negation,[status(cth)],[thm_2Einteger_2EINT__DIVIDES__RSUB]) ).
thf(h1,assumption,
~ ! [X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ X1 )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ ( mono_2Ec_2Einteger_2Eint__sub @ X2 @ X1 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: mono_2Etyop_2Einteger_2Eint] :
( sP7
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ ( mono_2Ec_2Einteger_2Eint__sub @ X1 @ eigen__1 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ eigen__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP7
=> ( sP5 = sP18 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP7,
introduced(assumption,[]) ).
thf(h5,assumption,
sP5 != sP18,
introduced(assumption,[]) ).
thf(h6,assumption,
sP5,
introduced(assumption,[]) ).
thf(h7,assumption,
sP18,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP19
| ~ sP4
| sP17 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP13
| ~ sP19
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP15
| ~ sP6
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP12
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
~ sP17,
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP9
| sP6
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP11
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP2
| ~ sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP16
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP1
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(thm_2Einteger_2EINT__DIVIDES__NEG,axiom,
sP8 ).
thf(thm_2Einteger_2EINT__DIVIDES__RADD,axiom,
sP1 ).
thf(thm_2Einteger_2Eint__sub,axiom,
sP10 ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h4,h6,h7,thm_2Einteger_2EINT__DIVIDES__NEG,thm_2Einteger_2EINT__DIVIDES__RADD,thm_2Einteger_2Eint__sub]) ).
thf(15,plain,
( ~ sP19
| sP5
| ~ sP14
| sP17 ),
inference(mating_rule,[status(thm)],]) ).
thf(16,plain,
~ sP17,
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP13
| sP19
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP15
| ~ sP6
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP9
| sP6
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP11
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP3
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP2
| ~ sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP12
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP1
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP4
| sP14 ),
inference(symeq,[status(thm)],]) ).
thf(27,plain,
( ~ sP16
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP10
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h4,h5,h3,h2,h1,h0])],[15,16,17,18,19,20,21,22,23,24,25,26,27,28,h4,h8,h9,thm_2Einteger_2EINT__DIVIDES__NEG,thm_2Einteger_2EINT__DIVIDES__RADD,thm_2Einteger_2Eint__sub]) ).
thf(30,plain,
$false,
inference(tab_be,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_be(discharge,[h6,h7]),tab_be(discharge,[h8,h9])],[h5,14,29,h6,h7,h8,h9]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,30,h4,h5]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,31,h3]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,32,h2]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,33,h1]) ).
thf(0,theorem,
! [X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint,X3: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2 )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ ( mono_2Ec_2Einteger_2Eint__sub @ X3 @ X2 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X3 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[34,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP012^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 13:00:18 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.46/1.66 % SZS status Theorem
% 1.46/1.66 % Mode: cade22sinegrackle2x6978
% 1.46/1.66 % Steps: 14873
% 1.46/1.66 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------