TSTP Solution File: NUM314+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM314+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n003.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 12:00:23 EDT 2023
% Result : Theorem 55.48s 8.39s
% Output : Refutation 55.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 91 ( 30 unt; 0 def)
% Number of atoms : 261 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 332 ( 162 ~; 137 |; 18 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 10 usr; 5 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 237 (; 235 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f37323,plain,
$false,
inference(avatar_sat_refutation,[],[f4179,f17536,f35774,f35793,f37322]) ).
fof(f37322,plain,
~ spl0_1751,
inference(avatar_contradiction_clause,[],[f37321]) ).
fof(f37321,plain,
( $false
| ~ spl0_1751 ),
inference(subsumption_resolution,[],[f37320,f771]) ).
fof(f771,plain,
rdn_digit_add(rdnn(n2),rdnn(n0),rdnn(n2),rdnn(n0)),
inference(cnf_transformation,[],[f322]) ).
fof(f322,axiom,
rdn_digit_add(rdnn(n2),rdnn(n0),rdnn(n2),rdnn(n0)),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',rdn_digit_add_n2_n0_n2_n0) ).
fof(f37320,plain,
( ~ rdn_digit_add(rdnn(n2),rdnn(n0),rdnn(n2),rdnn(n0))
| ~ spl0_1751 ),
inference(resolution,[],[f37303,f780]) ).
fof(f780,plain,
rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(n2),rdnn(n0)),
inference(cnf_transformation,[],[f304]) ).
fof(f304,axiom,
rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(n2),rdnn(n0)),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',rdn_digit_add_n0_n2_n2_n0) ).
fof(f37303,plain,
( ! [X0] :
( ~ rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(n2),rdnn(n0)) )
| ~ spl0_1751 ),
inference(resolution,[],[f37286,f781]) ).
fof(f781,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(cnf_transformation,[],[f302]) ).
fof(f302,axiom,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',rdn_digit_add_n0_n0_n0_n0) ).
fof(f37286,plain,
( ! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(n2),rdnn(X1))
| ~ rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(X2),rdnn(X0)) )
| ~ spl0_1751 ),
inference(resolution,[],[f37269,f791]) ).
fof(f791,plain,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
inference(cnf_transformation,[],[f312]) ).
fof(f312,axiom,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',rdn_digit_add_n1_n0_n1_n0) ).
fof(f37269,plain,
( ! [X2,X3,X0,X1] :
( ~ rdn_digit_add(rdnn(n1),rdnn(X3),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X2),rdnn(X1),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(n2),rdnn(X1))
| ~ rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(X0),rdnn(X2)) )
| ~ spl0_1751 ),
inference(resolution,[],[f35810,f782]) ).
fof(f782,plain,
rdn_digit_add(rdnn(n0),rdnn(n1),rdnn(n1),rdnn(n0)),
inference(cnf_transformation,[],[f303]) ).
fof(f303,axiom,
rdn_digit_add(rdnn(n0),rdnn(n1),rdnn(n1),rdnn(n0)),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',rdn_digit_add_n0_n1_n1_n0) ).
fof(f35810,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ rdn_digit_add(rdnn(n0),rdnn(n1),rdnn(X4),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(n2),rdnn(X2))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X4),rdnn(X3),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(X0),rdnn(X1)) )
| ~ spl0_1751 ),
inference(resolution,[],[f35770,f871]) ).
fof(f871,plain,
! [X2,X3,X0,X1,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
inference(cnf_transformation,[],[f456]) ).
fof(f456,plain,
! [X0,X1,X2,X3,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
inference(flattening,[],[f455]) ).
fof(f455,plain,
! [X0,X1,X2,X3,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
inference(ennf_transformation,[],[f416]) ).
fof(f416,plain,
! [X0,X1,X2,X3,X4] :
( ( rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
& rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
inference(rectify,[],[f297]) ).
fof(f297,axiom,
! [X20,X21,X22,X23,X24] :
( ( rdn_digit_add(rdnn(X24),rdnn(X20),rdnn(X23),rdnn(n0))
& rdn_digit_add(rdnn(X21),rdnn(X22),rdnn(X24),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(X20),rdnn(X21),rdnn(X22),rdnn(X23)) ),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',add_digit_digit_digit) ).
fof(f35770,plain,
( ! [X2,X3,X0,X1] :
( ~ rdn_add_with_carry(rdnn(X0),rdnn(n0),rdnn(n1),rdnn(n1))
| ~ rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(X3),rdnn(X1))
| ~ rdn_digit_add(rdnn(X3),rdnn(n0),rdnn(n2),rdnn(X2))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X0),rdnn(n0)) )
| ~ spl0_1751 ),
inference(avatar_component_clause,[],[f35769]) ).
fof(f35769,plain,
( spl0_1751
<=> ! [X0,X3,X2,X1] :
( ~ rdn_add_with_carry(rdnn(X0),rdnn(n0),rdnn(n1),rdnn(n1))
| ~ rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(X3),rdnn(X1))
| ~ rdn_digit_add(rdnn(X3),rdnn(n0),rdnn(n2),rdnn(X2))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X0),rdnn(n0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1751])]) ).
fof(f35793,plain,
spl0_1752,
inference(avatar_contradiction_clause,[],[f35792]) ).
fof(f35792,plain,
( $false
| spl0_1752 ),
inference(subsumption_resolution,[],[f35791,f484]) ).
fof(f484,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(cnf_transformation,[],[f257]) ).
fof(f257,axiom,
rdn_non_zero_digit(rdnn(n1)),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',rdn_digit1) ).
fof(f35791,plain,
( ~ rdn_non_zero_digit(rdnn(n1))
| spl0_1752 ),
inference(resolution,[],[f35773,f850]) ).
fof(f850,plain,
! [X0] :
( rdn_non_zero(rdnn(X0))
| ~ rdn_non_zero_digit(rdnn(X0)) ),
inference(cnf_transformation,[],[f427]) ).
fof(f427,plain,
! [X0] :
( rdn_non_zero(rdnn(X0))
| ~ rdn_non_zero_digit(rdnn(X0)) ),
inference(ennf_transformation,[],[f279]) ).
fof(f279,axiom,
! [X0] :
( rdn_non_zero_digit(rdnn(X0))
=> rdn_non_zero(rdnn(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',rdn_non_zero_by_digit) ).
fof(f35773,plain,
( ~ rdn_non_zero(rdnn(n1))
| spl0_1752 ),
inference(avatar_component_clause,[],[f35772]) ).
fof(f35772,plain,
( spl0_1752
<=> rdn_non_zero(rdnn(n1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1752])]) ).
fof(f35774,plain,
( spl0_1751
| ~ spl0_1752
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f32585,f4117,f35772,f35769]) ).
fof(f4117,plain,
( spl0_404
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),X2)))
| ~ rdn_digit_add(rdnn(n1),rdnn(n6),rdnn(X6),rdnn(X4))
| ~ rdn_digit_add(rdnn(X6),rdnn(n0),rdnn(X1),rdnn(X5))
| ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(X3),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(X3),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),X2)
| ~ rdn_non_zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f32585,plain,
( ! [X2,X3,X0,X1] :
( ~ rdn_non_zero(rdnn(n1))
| ~ rdn_add_with_carry(rdnn(X0),rdnn(n0),rdnn(n1),rdnn(n1))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X3),rdnn(n0),rdnn(n2),rdnn(X2))
| ~ rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(X3),rdnn(X1)) )
| ~ spl0_404 ),
inference(duplicate_literal_removal,[],[f32584]) ).
fof(f32584,plain,
( ! [X2,X3,X0,X1] :
( ~ rdn_non_zero(rdnn(n1))
| ~ rdn_non_zero(rdnn(n1))
| ~ rdn_add_with_carry(rdnn(X0),rdnn(n0),rdnn(n1),rdnn(n1))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X3),rdnn(n0),rdnn(n2),rdnn(X2))
| ~ rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(X3),rdnn(X1)) )
| ~ spl0_404 ),
inference(resolution,[],[f32511,f878]) ).
fof(f878,plain,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdn(rdnn(X2),X3),rdn(rdnn(X4),X5))
| ~ rdn_non_zero(X5)
| ~ rdn_non_zero(X3)
| ~ rdn_add_with_carry(rdnn(X9),rdnn(n0),X3,X5)
| ~ rdn_digit_add(rdnn(X7),rdnn(X8),rdnn(X9),rdnn(n0))
| ~ rdn_digit_add(rdnn(X6),rdnn(X0),rdnn(X4),rdnn(X8))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X6),rdnn(X7)) ),
inference(cnf_transformation,[],[f469]) ).
fof(f469,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdn(rdnn(X2),X3),rdn(rdnn(X4),X5))
| ~ rdn_non_zero(X5)
| ~ rdn_non_zero(X3)
| ~ rdn_add_with_carry(rdnn(X9),rdnn(n0),X3,X5)
| ~ rdn_digit_add(rdnn(X7),rdnn(X8),rdnn(X9),rdnn(n0))
| ~ rdn_digit_add(rdnn(X6),rdnn(X0),rdnn(X4),rdnn(X8))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X6),rdnn(X7)) ),
inference(flattening,[],[f468]) ).
fof(f468,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdn(rdnn(X2),X3),rdn(rdnn(X4),X5))
| ~ rdn_non_zero(X5)
| ~ rdn_non_zero(X3)
| ~ rdn_add_with_carry(rdnn(X9),rdnn(n0),X3,X5)
| ~ rdn_digit_add(rdnn(X7),rdnn(X8),rdnn(X9),rdnn(n0))
| ~ rdn_digit_add(rdnn(X6),rdnn(X0),rdnn(X4),rdnn(X8))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X6),rdnn(X7)) ),
inference(ennf_transformation,[],[f423]) ).
fof(f423,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( rdn_non_zero(X5)
& rdn_non_zero(X3)
& rdn_add_with_carry(rdnn(X9),rdnn(n0),X3,X5)
& rdn_digit_add(rdnn(X7),rdnn(X8),rdnn(X9),rdnn(n0))
& rdn_digit_add(rdnn(X6),rdnn(X0),rdnn(X4),rdnn(X8))
& rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X6),rdnn(X7)) )
=> rdn_add_with_carry(rdnn(X0),rdnn(X1),rdn(rdnn(X2),X3),rdn(rdnn(X4),X5)) ),
inference(rectify,[],[f299]) ).
fof(f299,axiom,
! [X20,X21,X22,X27,X23,X28,X24,X25,X26,X29] :
( ( rdn_non_zero(X28)
& rdn_non_zero(X27)
& rdn_add_with_carry(rdnn(X29),rdnn(n0),X27,X28)
& rdn_digit_add(rdnn(X25),rdnn(X26),rdnn(X29),rdnn(n0))
& rdn_digit_add(rdnn(X24),rdnn(X20),rdnn(X23),rdnn(X26))
& rdn_digit_add(rdnn(X21),rdnn(X22),rdnn(X24),rdnn(X25)) )
=> rdn_add_with_carry(rdnn(X20),rdnn(X21),rdn(rdnn(X22),X27),rdn(rdnn(X23),X28)) ),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',add_digit_rdn_rdn) ).
fof(f32511,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(n2),rdnn(n1)))
| ~ spl0_404 ),
inference(resolution,[],[f32510,f808]) ).
fof(f808,plain,
rdn_translate(n127,rdn_pos(rdn(rdnn(n7),rdn(rdnn(n2),rdnn(n1))))),
inference(cnf_transformation,[],[f128]) ).
fof(f128,axiom,
rdn_translate(n127,rdn_pos(rdn(rdnn(n7),rdn(rdnn(n2),rdnn(n1))))),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',rdn127) ).
fof(f32510,plain,
( ! [X0,X1] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(n7),rdn(rdnn(X1),rdnn(n1)))))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(X1),rdnn(n1))) )
| ~ spl0_404 ),
inference(subsumption_resolution,[],[f32500,f789]) ).
fof(f789,plain,
rdn_digit_add(rdnn(n1),rdnn(n6),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[],[f318]) ).
fof(f318,axiom,
rdn_digit_add(rdnn(n1),rdnn(n6),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',rdn_digit_add_n1_n6_n7_n0) ).
fof(f32500,plain,
( ! [X0,X1] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(n7),rdn(rdnn(X1),rdnn(n1)))))
| ~ rdn_digit_add(rdnn(n1),rdnn(n6),rdnn(n7),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(X1),rdnn(n1))) )
| ~ spl0_404 ),
inference(resolution,[],[f19929,f781]) ).
fof(f19929,plain,
( ! [X31,X28,X29,X30] :
( ~ rdn_digit_add(rdnn(X31),rdnn(n0),rdnn(X28),rdnn(n0))
| ~ rdn_translate(X30,rdn_pos(rdn(rdnn(n7),rdn(rdnn(X29),rdnn(n1)))))
| ~ rdn_digit_add(rdnn(n1),rdnn(n6),rdnn(n7),rdnn(X31))
| ~ rdn_add_with_carry(rdnn(X28),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(X29),rdnn(n1))) )
| ~ spl0_404 ),
inference(resolution,[],[f17652,f754]) ).
fof(f754,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[],[f372]) ).
fof(f372,axiom,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',rdn_digit_add_n7_n0_n7_n0) ).
fof(f17652,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_digit_add(rdnn(X6),rdnn(n0),rdnn(X5),rdnn(X1))
| ~ rdn_add_with_carry(rdnn(X2),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(X3),rdnn(n1)))
| ~ rdn_translate(X4,rdn_pos(rdn(rdnn(X5),rdn(rdnn(X3),rdnn(n1)))))
| ~ rdn_digit_add(rdnn(n1),rdnn(n6),rdnn(X6),rdnn(X0))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) )
| ~ spl0_404 ),
inference(resolution,[],[f17548,f484]) ).
fof(f17548,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ rdn_non_zero_digit(rdnn(X6))
| ~ rdn_digit_add(rdnn(X3),rdnn(X2),rdnn(X4),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(X4),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(X5),rdnn(X6)))
| ~ rdn_translate(X7,rdn_pos(rdn(rdnn(X1),rdn(rdnn(X5),rdnn(X6)))))
| ~ rdn_digit_add(rdnn(n1),rdnn(n6),rdnn(X0),rdnn(X3))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(X2)) )
| ~ spl0_404 ),
inference(resolution,[],[f17538,f850]) ).
fof(f17538,plain,
( ! [X10,X11,X8,X9,X7,X14,X12,X13] :
( ~ rdn_non_zero(X13)
| ~ rdn_digit_add(rdnn(X7),rdnn(n0),rdnn(X9),rdnn(X10))
| ~ rdn_digit_add(rdnn(X8),rdnn(X10),rdnn(X11),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(X11),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(X12),X13))
| ~ rdn_translate(X14,rdn_pos(rdn(rdnn(X9),rdn(rdnn(X12),X13))))
| ~ rdn_digit_add(rdnn(n1),rdnn(n6),rdnn(X7),rdnn(X8)) )
| ~ spl0_404 ),
inference(resolution,[],[f4118,f851]) ).
fof(f851,plain,
! [X0,X1] :
( rdn_non_zero(rdn(rdnn(X0),X1))
| ~ rdn_non_zero(X1) ),
inference(cnf_transformation,[],[f428]) ).
fof(f428,plain,
! [X0,X1] :
( rdn_non_zero(rdn(rdnn(X0),X1))
| ~ rdn_non_zero(X1) ),
inference(ennf_transformation,[],[f404]) ).
fof(f404,plain,
! [X0,X1] :
( rdn_non_zero(X1)
=> rdn_non_zero(rdn(rdnn(X0),X1)) ),
inference(rectify,[],[f280]) ).
fof(f280,axiom,
! [X8,X7] :
( rdn_non_zero(X7)
=> rdn_non_zero(rdn(rdnn(X8),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',rdn_non_zero_by_structure) ).
fof(f4118,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_non_zero(X2)
| ~ rdn_digit_add(rdnn(n1),rdnn(n6),rdnn(X6),rdnn(X4))
| ~ rdn_digit_add(rdnn(X6),rdnn(n0),rdnn(X1),rdnn(X5))
| ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(X3),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(X3),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),X2)
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),X2))) )
| ~ spl0_404 ),
inference(avatar_component_clause,[],[f4117]) ).
fof(f17536,plain,
( ~ spl0_403
| spl0_404 ),
inference(avatar_split_clause,[],[f1258,f4117,f4114]) ).
fof(f4114,plain,
( spl0_403
<=> rdn_non_zero(rdn(rdnn(n2),rdnn(n1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f1258,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),X2)))
| ~ rdn_non_zero(X2)
| ~ rdn_non_zero(rdn(rdnn(n2),rdnn(n1)))
| ~ rdn_add_with_carry(rdnn(X3),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),X2)
| ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X6),rdnn(n0),rdnn(X1),rdnn(X5))
| ~ rdn_digit_add(rdnn(n1),rdnn(n6),rdnn(X6),rdnn(X4)) ),
inference(resolution,[],[f986,f878]) ).
fof(f986,plain,
! [X2,X0,X1] :
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n1),rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))),rdn(rdnn(X1),X2))
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),X2))) ),
inference(resolution,[],[f937,f872]) ).
fof(f872,plain,
! [X2,X3,X0,X1,X4,X5] :
( rdn_add_with_carry(rdnn(X0),rdn(rdnn(X1),X2),rdnn(X3),rdn(rdnn(X4),X5))
| ~ rdn_add_with_carry(rdnn(X0),rdnn(X3),rdn(rdnn(X1),X2),rdn(rdnn(X4),X5)) ),
inference(cnf_transformation,[],[f457]) ).
fof(f457,plain,
! [X0,X1,X2,X3,X4,X5] :
( rdn_add_with_carry(rdnn(X0),rdn(rdnn(X1),X2),rdnn(X3),rdn(rdnn(X4),X5))
| ~ rdn_add_with_carry(rdnn(X0),rdnn(X3),rdn(rdnn(X1),X2),rdn(rdnn(X4),X5)) ),
inference(ennf_transformation,[],[f417]) ).
fof(f417,plain,
! [X0,X1,X2,X3,X4,X5] :
( rdn_add_with_carry(rdnn(X0),rdnn(X3),rdn(rdnn(X1),X2),rdn(rdnn(X4),X5))
=> rdn_add_with_carry(rdnn(X0),rdn(rdnn(X1),X2),rdnn(X3),rdn(rdnn(X4),X5)) ),
inference(rectify,[],[f301]) ).
fof(f301,axiom,
! [X20,X21,X30,X22,X23,X28] :
( rdn_add_with_carry(rdnn(X20),rdnn(X22),rdn(rdnn(X21),X30),rdn(rdnn(X23),X28))
=> rdn_add_with_carry(rdnn(X20),rdn(rdnn(X21),X30),rdnn(X22),rdn(rdnn(X23),X28)) ),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',add_rdn_digit_rdn) ).
fof(f937,plain,
! [X0,X1] :
( ~ rdn_add_with_carry(rdnn(n0),rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))),rdnn(n1),X0)
| ~ rdn_translate(X1,rdn_pos(X0)) ),
inference(resolution,[],[f909,f512]) ).
fof(f512,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',rdn1) ).
fof(f909,plain,
! [X2,X0,X1] :
( ~ rdn_translate(n1,rdn_pos(X0))
| ~ rdn_add_with_carry(rdnn(n0),rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))),X0,X1)
| ~ rdn_translate(X2,rdn_pos(X1)) ),
inference(resolution,[],[f882,f849]) ).
fof(f849,plain,
rdn_translate(n126,rdn_pos(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))))),
inference(cnf_transformation,[],[f127]) ).
fof(f127,axiom,
rdn_translate(n126,rdn_pos(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))))),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',rdn126) ).
fof(f882,plain,
! [X2,X3,X1,X4] :
( ~ rdn_translate(n126,rdn_pos(X3))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X2)
| ~ rdn_translate(n1,rdn_pos(X4))
| ~ rdn_translate(X1,rdn_pos(X2)) ),
inference(resolution,[],[f475,f876]) ).
fof(f876,plain,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(cnf_transformation,[],[f465]) ).
fof(f465,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(flattening,[],[f464]) ).
fof(f464,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(ennf_transformation,[],[f421]) ).
fof(f421,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X2,rdn_pos(X5))
& rdn_add_with_carry(rdnn(n0),X3,X4,X5)
& rdn_translate(X1,rdn_pos(X4))
& rdn_translate(X0,rdn_pos(X3)) )
=> sum(X0,X1,X2) ),
inference(rectify,[],[f287]) ).
fof(f287,axiom,
! [X0,X1,X2,X9,X10,X11] :
( ( rdn_translate(X2,rdn_pos(X11))
& rdn_add_with_carry(rdnn(n0),X9,X10,X11)
& rdn_translate(X1,rdn_pos(X10))
& rdn_translate(X0,rdn_pos(X9)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',sum_entry_point_pos_pos) ).
fof(f475,plain,
! [X0] : ~ sum(n126,n1,X0),
inference(cnf_transformation,[],[f426]) ).
fof(f426,plain,
! [X0] : ~ sum(n126,n1,X0),
inference(ennf_transformation,[],[f403]) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(n126,n1,X0),
inference(negated_conjecture,[],[f402]) ).
fof(f402,conjecture,
? [X0] : sum(n126,n1,X0),
file('/export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168',show_upper_boundary) ).
fof(f4179,plain,
spl0_403,
inference(avatar_contradiction_clause,[],[f4178]) ).
fof(f4178,plain,
( $false
| spl0_403 ),
inference(subsumption_resolution,[],[f4177,f484]) ).
fof(f4177,plain,
( ~ rdn_non_zero_digit(rdnn(n1))
| spl0_403 ),
inference(resolution,[],[f4120,f850]) ).
fof(f4120,plain,
( ~ rdn_non_zero(rdnn(n1))
| spl0_403 ),
inference(resolution,[],[f4115,f851]) ).
fof(f4115,plain,
( ~ rdn_non_zero(rdn(rdnn(n2),rdnn(n1)))
| spl0_403 ),
inference(avatar_component_clause,[],[f4114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.15 % Problem : NUM314+1 : TPTP v8.1.2. Released v3.1.0.
% 0.11/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.38 % Computer : n003.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Fri Aug 25 13:56:08 EDT 2023
% 0.15/0.38 % CPUTime :
% 0.15/0.39 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.39 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.FHlDZwwFhZ/Vampire---4.8_3168
% 0.15/0.39 % (3310)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.46 % (3321)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.24/0.46 % (3313)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.24/0.46 % (3318)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.24/0.46 % (3319)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.24/0.46 % (3320)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.24/0.46 % (3316)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.24/0.46 % (3322)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.24/0.47 % (3322)Refutation not found, incomplete strategy% (3322)------------------------------
% 0.24/0.47 % (3322)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.47 % (3322)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.47 % (3322)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.47
% 0.24/0.47 % (3322)Memory used [KB]: 6140
% 0.24/0.47 % (3322)Time elapsed: 0.011 s
% 0.24/0.47 % (3322)------------------------------
% 0.24/0.47 % (3322)------------------------------
% 0.24/0.47 % (3313)Refutation not found, incomplete strategy% (3313)------------------------------
% 0.24/0.47 % (3313)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.47 % (3313)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.47 % (3313)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.47
% 0.24/0.47 % (3313)Memory used [KB]: 6396
% 0.24/0.47 % (3313)Time elapsed: 0.014 s
% 0.24/0.47 % (3313)------------------------------
% 0.24/0.47 % (3313)------------------------------
% 0.24/0.52 % (3323)lrs-11_32_amm=off:bce=on:cond=on:er=filter:fsd=off:fde=none:gs=on:gsem=on:lcm=reverse:nm=4:nwc=1.1:sos=all:sac=on:sp=frequency:urr=on:stl=125_403 on Vampire---4 for (403ds/0Mi)
% 0.24/0.53 % (3324)lrs+1010_5:1_bd=off:fsd=off:fde=unused:lcm=predicate:nm=64:nwc=1.7:sac=on:sp=frequency:tgt=ground:stl=62_333 on Vampire---4 for (333ds/0Mi)
% 55.48/8.37 % (3320)First to succeed.
% 55.48/8.39 % (3320)Refutation found. Thanks to Tanya!
% 55.48/8.39 % SZS status Theorem for Vampire---4
% 55.48/8.39 % SZS output start Proof for Vampire---4
% See solution above
% 55.48/8.39 % (3320)------------------------------
% 55.48/8.39 % (3320)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 55.48/8.39 % (3320)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 55.48/8.39 % (3320)Termination reason: Refutation
% 55.48/8.39
% 55.48/8.39 % (3320)Memory used [KB]: 79828
% 55.48/8.39 % (3320)Time elapsed: 7.923 s
% 55.48/8.39 % (3320)------------------------------
% 55.48/8.39 % (3320)------------------------------
% 55.48/8.39 % (3310)Success in time 7.994 s
% 55.48/8.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------