TSTP Solution File: NUM339+1 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : NUM339+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n023.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 : Mon Jun 24 13:12:28 EDT 2024
% Result : Theorem 1.03s 0.53s
% Output : Refutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 94 ( 30 unt; 0 def)
% Number of atoms : 285 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 369 ( 178 ~; 154 |; 21 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 13 ( 12 usr; 5 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 228 ( 226 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f949,plain,
$false,
inference(avatar_sat_refutation,[],[f919,f923,f936,f939,f948]) ).
fof(f948,plain,
( ~ spl1_5
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[],[f947]) ).
fof(f947,plain,
( $false
| ~ spl1_5
| ~ spl1_6 ),
inference(subsumption_resolution,[],[f946,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/benchmark/theBenchmark.p',unknown) ).
fof(f946,plain,
( ~ rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0))
| ~ spl1_5
| ~ spl1_6 ),
inference(resolution,[],[f945,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/benchmark/theBenchmark.p',unknown) ).
fof(f945,plain,
( ! [X0] :
( ~ rdn_digit_add(rdnn(n0),rdnn(n1),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(n1),rdnn(n0)) )
| ~ spl1_5
| ~ spl1_6 ),
inference(resolution,[],[f944,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/benchmark/theBenchmark.p',unknown) ).
fof(f944,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n0),rdnn(n1),rdnn(n1))
| ~ spl1_5
| ~ spl1_6 ),
inference(subsumption_resolution,[],[f943,f931]) ).
fof(f931,plain,
( rdn_non_zero(rdnn(n1))
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f930]) ).
fof(f930,plain,
( spl1_5
<=> rdn_non_zero(rdnn(n1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f943,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n0),rdnn(n1),rdnn(n1))
| ~ rdn_non_zero(rdnn(n1))
| ~ spl1_6 ),
inference(resolution,[],[f942,f797]) ).
fof(f797,plain,
rdn_translate(nn128,rdn_neg(rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1))))),
inference(cnf_transformation,[],[f256]) ).
fof(f256,axiom,
rdn_translate(nn128,rdn_neg(rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f942,plain,
( ! [X0,X1] :
( ~ rdn_translate(X0,rdn_neg(rdn(rdnn(n8),rdn(rdnn(n2),X1))))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n0),rdnn(n1),X1)
| ~ rdn_non_zero(X1) )
| ~ spl1_6 ),
inference(resolution,[],[f941,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/benchmark/theBenchmark.p',unknown) ).
fof(f941,plain,
( ! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(X2),rdnn(n0))
| ~ rdn_translate(X0,rdn_neg(rdn(rdnn(n8),rdn(rdnn(n2),X1))))
| ~ rdn_add_with_carry(rdnn(X2),rdnn(n0),rdnn(n1),X1)
| ~ rdn_non_zero(X1) )
| ~ spl1_6 ),
inference(resolution,[],[f940,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/benchmark/theBenchmark.p',unknown) ).
fof(f940,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ rdn_digit_add(rdnn(n2),rdnn(n0),rdnn(X1),rdnn(X3))
| ~ rdn_translate(X0,rdn_neg(rdn(rdnn(n8),rdn(rdnn(X1),X2))))
| ~ rdn_digit_add(rdnn(n0),rdnn(X3),rdnn(X4),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(X4),rdnn(n0),rdnn(n1),X2)
| ~ rdn_non_zero(X2) )
| ~ spl1_6 ),
inference(resolution,[],[f935,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/benchmark/theBenchmark.p',unknown) ).
fof(f935,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(X6),rdnn(X4))
| ~ rdn_translate(X0,rdn_neg(rdn(rdnn(n8),rdn(rdnn(X1),X2))))
| ~ 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),rdnn(n1),X2)
| ~ rdn_non_zero(X2) )
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f934,plain,
( spl1_6
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ rdn_translate(X0,rdn_neg(rdn(rdnn(n8),rdn(rdnn(X1),X2))))
| ~ rdn_digit_add(rdnn(n0),rdnn(n2),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),rdnn(n1),X2)
| ~ rdn_non_zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f939,plain,
spl1_5,
inference(avatar_contradiction_clause,[],[f938]) ).
fof(f938,plain,
( $false
| spl1_5 ),
inference(subsumption_resolution,[],[f937,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/benchmark/theBenchmark.p',unknown) ).
fof(f937,plain,
( ~ rdn_non_zero_digit(rdnn(n1))
| spl1_5 ),
inference(resolution,[],[f932,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/benchmark/theBenchmark.p',unknown) ).
fof(f932,plain,
( ~ rdn_non_zero(rdnn(n1))
| spl1_5 ),
inference(avatar_component_clause,[],[f930]) ).
fof(f936,plain,
( ~ spl1_5
| spl1_6
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f928,f917,f934,f930]) ).
fof(f917,plain,
( spl1_4
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ rdn_translate(X0,rdn_neg(rdn(rdnn(X1),X2)))
| ~ rdn_digit_add(rdnn(n1),rdnn(n7),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,[spl1_4])]) ).
fof(f928,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_translate(X0,rdn_neg(rdn(rdnn(n8),rdn(rdnn(X1),X2))))
| ~ rdn_non_zero(X2)
| ~ rdn_non_zero(rdnn(n1))
| ~ rdn_add_with_carry(rdnn(X3),rdnn(n0),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(n0),rdnn(n2),rdnn(X6),rdnn(X4)) )
| ~ spl1_4 ),
inference(subsumption_resolution,[],[f927,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/benchmark/theBenchmark.p',unknown) ).
fof(f927,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_translate(X0,rdn_neg(rdn(rdnn(n8),rdn(rdnn(X1),X2))))
| ~ rdn_non_zero(rdn(rdnn(X1),X2))
| ~ rdn_non_zero(X2)
| ~ rdn_non_zero(rdnn(n1))
| ~ rdn_add_with_carry(rdnn(X3),rdnn(n0),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(n0),rdnn(n2),rdnn(X6),rdnn(X4)) )
| ~ spl1_4 ),
inference(resolution,[],[f926,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/benchmark/theBenchmark.p',unknown) ).
fof(f926,plain,
( ! [X0,X1] :
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),X1)
| ~ rdn_translate(X0,rdn_neg(rdn(rdnn(n8),X1)))
| ~ rdn_non_zero(X1) )
| ~ spl1_4 ),
inference(resolution,[],[f925,f781]) ).
fof(f925,plain,
( ! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(X2),rdnn(n0))
| ~ rdn_translate(X0,rdn_neg(rdn(rdnn(n8),X1)))
| ~ rdn_add_with_carry(rdnn(X2),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),X1)
| ~ rdn_non_zero(X1) )
| ~ spl1_4 ),
inference(resolution,[],[f924,f711]) ).
fof(f711,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f382]) ).
fof(f382,axiom,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f924,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(X1),rdnn(X3))
| ~ rdn_translate(X0,rdn_neg(rdn(rdnn(X1),X2)))
| ~ rdn_digit_add(rdnn(n0),rdnn(X3),rdnn(X4),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(X4),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),X2)
| ~ rdn_non_zero(X2) )
| ~ spl1_4 ),
inference(resolution,[],[f918,f785]) ).
fof(f785,plain,
rdn_digit_add(rdnn(n1),rdnn(n7),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f319]) ).
fof(f319,axiom,
rdn_digit_add(rdnn(n1),rdnn(n7),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f918,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_digit_add(rdnn(n1),rdnn(n7),rdnn(X6),rdnn(X4))
| ~ rdn_translate(X0,rdn_neg(rdn(rdnn(X1),X2)))
| ~ 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) )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f917]) ).
fof(f923,plain,
spl1_3,
inference(avatar_contradiction_clause,[],[f922]) ).
fof(f922,plain,
( $false
| spl1_3 ),
inference(subsumption_resolution,[],[f921,f484]) ).
fof(f921,plain,
( ~ rdn_non_zero_digit(rdnn(n1))
| spl1_3 ),
inference(resolution,[],[f920,f850]) ).
fof(f920,plain,
( ~ rdn_non_zero(rdnn(n1))
| spl1_3 ),
inference(resolution,[],[f915,f851]) ).
fof(f915,plain,
( ~ rdn_non_zero(rdn(rdnn(n2),rdnn(n1)))
| spl1_3 ),
inference(avatar_component_clause,[],[f913]) ).
fof(f913,plain,
( spl1_3
<=> rdn_non_zero(rdn(rdnn(n2),rdnn(n1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f919,plain,
( ~ spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f911,f917,f913]) ).
fof(f911,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_translate(X0,rdn_neg(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(n7),rdnn(X6),rdnn(X4)) ),
inference(subsumption_resolution,[],[f910,f856]) ).
fof(f856,plain,
! [X2,X0,X1] :
( rdn_positive_less(rdnn(X0),rdn(rdnn(X1),X2))
| ~ rdn_non_zero(X2) ),
inference(cnf_transformation,[],[f431]) ).
fof(f431,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X0),rdn(rdnn(X1),X2))
| ~ rdn_non_zero(X2) ),
inference(ennf_transformation,[],[f405]) ).
fof(f405,plain,
! [X0,X1,X2] :
( rdn_non_zero(X2)
=> rdn_positive_less(rdnn(X0),rdn(rdnn(X1),X2)) ),
inference(rectify,[],[f278]) ).
fof(f278,axiom,
! [X8,X5,X6] :
( rdn_non_zero(X6)
=> rdn_positive_less(rdnn(X8),rdn(rdnn(X5),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f910,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_translate(X0,rdn_neg(rdn(rdnn(X1),X2)))
| ~ rdn_positive_less(rdnn(n1),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(n7),rdnn(X6),rdnn(X4)) ),
inference(resolution,[],[f909,f878]) ).
fof(f909,plain,
! [X0,X1] :
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n1),rdn(rdnn(n7),rdn(rdnn(n2),rdnn(n1))),X0)
| ~ rdn_translate(X1,rdn_neg(X0))
| ~ rdn_positive_less(rdnn(n1),X0) ),
inference(resolution,[],[f908,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/benchmark/theBenchmark.p',unknown) ).
fof(f908,plain,
! [X2,X0,X1] :
( ~ rdn_translate(n1,rdn_pos(X0))
| ~ rdn_positive_less(X0,X1)
| ~ rdn_translate(X2,rdn_neg(X1))
| ~ rdn_add_with_carry(rdnn(n0),X0,rdn(rdnn(n7),rdn(rdnn(n2),rdnn(n1))),X1) ),
inference(resolution,[],[f893,f849]) ).
fof(f849,plain,
rdn_translate(nn127,rdn_neg(rdn(rdnn(n7),rdn(rdnn(n2),rdnn(n1))))),
inference(cnf_transformation,[],[f255]) ).
fof(f255,axiom,
rdn_translate(nn127,rdn_neg(rdn(rdnn(n7),rdn(rdnn(n2),rdnn(n1))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f893,plain,
! [X2,X3,X0,X1] :
( ~ rdn_translate(nn127,rdn_neg(X0))
| ~ rdn_add_with_carry(rdnn(n0),X1,X0,X2)
| ~ rdn_positive_less(X1,X2)
| ~ rdn_translate(X3,rdn_neg(X2))
| ~ rdn_translate(n1,rdn_pos(X1)) ),
inference(resolution,[],[f890,f874]) ).
fof(f874,plain,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(cnf_transformation,[],[f461]) ).
fof(f461,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(flattening,[],[f460]) ).
fof(f460,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(ennf_transformation,[],[f419]) ).
fof(f419,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X2,rdn_neg(X5))
& rdn_add_with_carry(rdnn(n0),X3,X5,X4)
& rdn_positive_less(X3,X4)
& rdn_translate(X1,rdn_neg(X4))
& rdn_translate(X0,rdn_pos(X3)) )
=> sum(X0,X1,X2) ),
inference(rectify,[],[f289]) ).
fof(f289,axiom,
! [X0,X1,X2,X9,X10,X11] :
( ( rdn_translate(X2,rdn_neg(X11))
& rdn_add_with_carry(rdnn(n0),X9,X11,X10)
& rdn_positive_less(X9,X10)
& rdn_translate(X1,rdn_neg(X10))
& rdn_translate(X0,rdn_pos(X9)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f890,plain,
! [X0] : ~ sum(n1,X0,nn127),
inference(resolution,[],[f475,f861]) ).
fof(f861,plain,
! [X2,X0,X1] :
( difference(X0,X1,X2)
| ~ sum(X1,X2,X0) ),
inference(cnf_transformation,[],[f474]) ).
fof(f474,plain,
! [X0,X1,X2] :
( ( sum(X1,X2,X0)
| ~ difference(X0,X1,X2) )
& ( difference(X0,X1,X2)
| ~ sum(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f296]) ).
fof(f296,axiom,
! [X0,X1,X2] :
( sum(X1,X2,X0)
<=> difference(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f475,plain,
! [X0] : ~ difference(nn127,n1,X0),
inference(cnf_transformation,[],[f426]) ).
fof(f426,plain,
! [X0] : ~ difference(nn127,n1,X0),
inference(ennf_transformation,[],[f403]) ).
fof(f403,negated_conjecture,
~ ? [X0] : difference(nn127,n1,X0),
inference(negated_conjecture,[],[f402]) ).
fof(f402,conjecture,
? [X0] : difference(nn127,n1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : NUM339+1 : TPTP v8.2.0. Released v3.1.0.
% 0.05/0.14 % Command : run_vampire %s %d THM
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Jun 23 03:10:39 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.23/0.38 This is a FOF_THM_RFO_SEQ problem
% 0.23/0.38 Running first-order theorem proving
% 0.23/0.38 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.46 % (18968)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.46 % (18972)lrs+10_1:3_drc=off:sil=256000:sp=unary_first:lwlo=on:i=216875:kws=precedence:ins=3:rawr=on:nwc=10.0_0 on theBenchmark for (2999ds/216875Mi)
% 0.23/0.46 % (18968)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.46 % (18971)lrs+1010_2201:262144_anc=all:drc=encompass:sil=256000:sims=off:sp=frequency:spb=goal_then_units:rp=on:lwlo=on:st=3.0:i=179501:bs=unit_only:nm=6:ins=2:fsd=on:ss=axioms:sgt=16:afr=on:tgt=ground:awrs=decay:awrsf=200:acc=on:ccuc=first_0 on theBenchmark for (2999ds/179501Mi)
% 0.23/0.46 % (18968)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.46 % (18974)dis+1010_1:1_sil=2000:nwc=3.0:s2a=on:i=132:ins=5:fsr=off:ss=axioms:sd=2:fd=off_0 on theBenchmark for (2999ds/132Mi)
% 0.23/0.46 % (18968)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.46 % (18975)dis+1010_159245:1048576_to=lpo:sil=2000:etr=on:sp=unary_frequency:spb=goal:rnwc=on:nwc=10.9066:st=2:i=124:sd=1:nm=3:av=off:ss=axioms:rawr=on:drc=encompass:foolp=on:sgt=5:cond=fast:er=filter:erape=on:erml=2:s2a=on_0 on theBenchmark for (2999ds/124Mi)
% 0.23/0.46 % (18968)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.46 % (18969)lrs+1011_1:12_anc=none:drc=off:sil=64000:sims=off:sp=unary_first:spb=goal_then_units:lsd=20:rnwc=on:nwc=2.0:i=53554:add=off:awrs=converge:bd=off:uhcvi=on:tgt=ground:afp=300:afq=1.63_0 on theBenchmark for (2999ds/53554Mi)
% 0.23/0.46 % (18968)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.46 % (18973)dis+1011_3:1_sil=256000:tgt=ground:sac=on:i=109:sd=1:ss=included_0 on theBenchmark for (2999ds/109Mi)
% 0.23/0.46 % (18968)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.46 % (18970)dis+11_1:1_nwc=5.0:s2a=on:i=66616:s2at=3.0:sil=128000:bd=off_0 on theBenchmark for (2999ds/66616Mi)
% 0.23/0.47 % (18973)Refutation not found, incomplete strategy% (18973)------------------------------
% 0.23/0.47 % (18973)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.23/0.47 % (18973)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.23/0.47 % (18973)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.47
% 0.23/0.47 % (18973)Memory used [KB]: 1307
% 0.23/0.47 % (18973)Time elapsed: 0.004 s
% 0.23/0.47 % (18973)Instructions burned: 3 (million)
% 0.23/0.47 % (18973)------------------------------
% 0.23/0.47 % (18973)------------------------------
% 0.23/0.47 % (18975)Refutation not found, incomplete strategy% (18975)------------------------------
% 0.23/0.47 % (18975)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.23/0.47 % (18975)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.23/0.47 % (18975)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.47
% 0.23/0.47 % (18975)Memory used [KB]: 1307
% 0.23/0.47 % (18975)Time elapsed: 0.004 s
% 0.23/0.47 % (18975)Instructions burned: 5 (million)
% 0.23/0.47 % (18974)Refutation not found, incomplete strategy% (18974)------------------------------
% 0.23/0.47 % (18974)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.23/0.47 % (18974)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.23/0.47 % (18974)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.47 % (18975)------------------------------
% 0.23/0.47 % (18975)------------------------------
% 0.23/0.47
% 0.23/0.47 % (18974)Memory used [KB]: 1320
% 0.23/0.47 % (18974)Time elapsed: 0.005 s
% 0.23/0.47 % (18974)Instructions burned: 5 (million)
% 0.23/0.47 % (18974)------------------------------
% 0.23/0.47 % (18974)------------------------------
% 0.23/0.51 % (18968)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.51 % (18977)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:st=1.5:i=145:ss=axioms:sgt=4_0 on theBenchmark for (2999ds/145Mi)
% 0.23/0.52 % (18968)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.52 % (18976)lrs+1011_1:1_sil=16000:sos=on:erd=off:i=126:nm=2:ep=RST_0 on theBenchmark for (2999ds/126Mi)
% 0.23/0.52 % (18968)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.52 % (18978)ott+1002_2835555:1048576_to=lpo:sil=2000:sos=on:fs=off:nwc=10.3801:avsqc=3:updr=off:avsq=on:st=2:s2a=on:i=173:s2at=3:afp=10000:aac=none:avsqr=13357983,1048576:awrs=converge:awrsf=460:bd=off:nm=13:ins=2:fsr=off:amm=sco:afq=1.16719:ss=axioms:rawr=on:fd=off_0 on theBenchmark for (2999ds/173Mi)
% 0.23/0.53 % (18978)Refutation not found, incomplete strategy% (18978)------------------------------
% 0.23/0.53 % (18978)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.23/0.53 % (18978)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.23/0.53 % (18978)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.53
% 0.23/0.53 % (18978)Memory used [KB]: 1352
% 0.23/0.53 % (18978)Time elapsed: 0.005 s
% 0.23/0.53 % (18978)Instructions burned: 10 (million)
% 0.23/0.53 % (18978)------------------------------
% 0.23/0.53 % (18978)------------------------------
% 1.03/0.53 % (18976)First to succeed.
% 1.03/0.53 % (18976)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18968"
% 1.03/0.53 % (18968)Running in auto input_syntax mode. Trying TPTP
% 1.03/0.53 % (18976)Refutation found. Thanks to Tanya!
% 1.03/0.53 % SZS status Theorem for theBenchmark
% 1.03/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 1.03/0.53 % (18976)------------------------------
% 1.03/0.53 % (18976)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.03/0.53 % (18976)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.03/0.53 % (18976)Termination reason: Refutation
% 1.03/0.53
% 1.03/0.53 % (18976)Memory used [KB]: 1550
% 1.03/0.53 % (18976)Time elapsed: 0.009 s
% 1.03/0.53 % (18976)Instructions burned: 22 (million)
% 1.03/0.53 % (18976)------------------------------
% 1.03/0.53 % (18976)------------------------------
% 1.03/0.53 % (18968)Success in time 0.133 s
%------------------------------------------------------------------------------