TSTP Solution File: ITP216^3 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP216^3 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 00:29:38 EDT 2022
% Result : Theorem 3.34s 3.55s
% Output : Proof 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 46
% Syntax : Number of formulae : 53 ( 13 unt; 17 typ; 2 def)
% Number of atoms : 73 ( 14 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 138 ( 29 ~; 12 |; 0 &; 74 @)
% ( 13 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 22 con; 0-2 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 21 ( 2 ^ 19 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_option3216581401566546698it_nat,type,
option3216581401566546698it_nat: $tType ).
thf(ty_heap_T6362127782908069795rray_a,type,
heap_T6362127782908069795rray_a: $tType ).
thf(ty_array_a,type,
array_a: $tType ).
thf(ty_heap_e7401611519738050253t_unit,type,
heap_e7401611519738050253t_unit: $tType ).
thf(ty_produc6653097349344004940it_nat,type,
produc6653097349344004940it_nat: $tType ).
thf(ty_produc6714399278180371524it_nat,type,
produc6714399278180371524it_nat: $tType ).
thf(ty_list_a,type,
list_a: $tType ).
thf(ty_h,type,
h: heap_e7401611519738050253t_unit ).
thf(ty_array_of_list_a,type,
array_of_list_a: list_a > heap_T6362127782908069795rray_a ).
thf(ty_eigen__1,type,
eigen__1: produc6653097349344004940it_nat ).
thf(ty_heap_T5591663578999710211rray_a,type,
heap_T5591663578999710211rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > option3216581401566546698it_nat ).
thf(ty_eigen__0,type,
eigen__0: array_a ).
thf(ty_heap_T6932021131025641745rray_a,type,
heap_T6932021131025641745rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > $o ).
thf(ty_produc1733996804261680252it_nat,type,
produc1733996804261680252it_nat: array_a > produc6653097349344004940it_nat > produc6714399278180371524it_nat ).
thf(ty_none_P2587165478634041381it_nat,type,
none_P2587165478634041381it_nat: option3216581401566546698it_nat ).
thf(ty_some_P6105628898608307625it_nat,type,
some_P6105628898608307625it_nat: produc6714399278180371524it_nat > option3216581401566546698it_nat ).
thf(ty_xs,type,
xs: list_a ).
thf(h0,assumption,
! [X1: produc6653097349344004940it_nat > $o,X2: produc6653097349344004940it_nat] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: produc6653097349344004940it_nat] :
~ ( ( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
!= ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ eigen__0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: array_a > $o,X2: array_a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: array_a] :
~ ! [X2: produc6653097349344004940it_nat] :
( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
!= ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: array_a,X2: produc6653097349344004940it_nat] :
( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
!= ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: list_a] : ( !! @ ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ xs ) @ h ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: heap_e7401611519738050253t_unit] :
( ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ xs ) @ X1 )
=> ~ ! [X2: array_a,X3: produc6653097349344004940it_nat] :
( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ X1 )
!= ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP3
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
= ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: produc6653097349344004940it_nat] :
( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
!= ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP6
=> ( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
!= none_P2587165478634041381it_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
= none_P2587165478634041381it_nat ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: produc6714399278180371524it_nat] :
( ( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
= ( some_P6105628898608307625it_nat @ X1 ) )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: option3216581401566546698it_nat,X2: produc6714399278180371524it_nat] :
( ( X1
= ( some_P6105628898608307625it_nat @ X2 ) )
=> ( X1 != none_P2587165478634041381it_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( !! @ ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ xs ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: heap_T6362127782908069795rray_a,X2: heap_e7401611519738050253t_unit] :
( ( heap_T6932021131025641745rray_a @ X1 @ X2 )
=> ~ ! [X3: array_a,X4: produc6653097349344004940it_nat] :
( ( heap_T5591663578999710211rray_a @ X1 @ X2 )
!= ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(conj_0,conjecture,
~ sP9 ).
thf(h2,negated_conjecture,
sP9,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP12
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| ~ sP3
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| ~ sP6
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP7
| sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(7,plain,
( sP1
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(8,plain,
( ~ sP2
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP13
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_119_successE,axiom,
sP13 ).
thf(fact_87_option_OdiscI,axiom,
sP11 ).
thf(fact_45_success__of__listI,axiom,
sP2 ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h2,fact_119_successE,fact_87_option_OdiscI,fact_45_success__of__listI]) ).
thf(12,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[11,h1]) ).
thf(13,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[12,h0]) ).
thf(0,theorem,
~ sP9,
inference(contra,[status(thm),contra(discharge,[h2])],[11,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP216^3 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jun 3 12:59:17 EDT 2022
% 0.14/0.35 % CPUTime :
% 3.34/3.55 % SZS status Theorem
% 3.34/3.55 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 3.34/3.55 % Inferences: 71
% 3.34/3.55 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------