TSTP Solution File: SWV007-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV007-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.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 : Sun May 5 10:41:04 EDT 2024
% Result : Unsatisfiable 0.11s 0.35s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 73
% Syntax : Number of formulae : 191 ( 35 unt; 0 def)
% Number of atoms : 510 ( 48 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 576 ( 257 ~; 267 |; 0 &)
% ( 52 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 55 ( 53 usr; 53 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-1 aty)
% Number of variables : 103 ( 103 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f480,plain,
$false,
inference(avatar_sat_refutation,[],[f30,f35,f40,f45,f50,f55,f60,f65,f69,f73,f78,f82,f91,f95,f99,f103,f107,f114,f123,f127,f137,f141,f174,f183,f189,f193,f202,f219,f258,f265,f270,f274,f284,f291,f295,f307,f322,f336,f340,f354,f358,f366,f383,f401,f406,f412,f413,f419,f438,f458,f463,f469,f474,f479]) ).
fof(f479,plain,
( ~ spl0_16
| spl0_49 ),
inference(avatar_contradiction_clause,[],[f475]) ).
fof(f475,plain,
( $false
| ~ spl0_16
| spl0_49 ),
inference(resolution,[],[f457,f98]) ).
fof(f98,plain,
( ! [X0] : less_than(X0,successor(X0))
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f97,plain,
( spl0_16
<=> ! [X0] : less_than(X0,successor(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f457,plain,
( ~ less_than(m,successor(m))
| spl0_49 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f455,plain,
( spl0_49
<=> less_than(m,successor(m)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f474,plain,
( ~ spl0_52
| ~ spl0_19
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f443,f380,f112,f471]) ).
fof(f471,plain,
( spl0_52
<=> less_than(m,one) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f112,plain,
( spl0_19
<=> ! [X0,X1] :
( ~ less_than(X1,X0)
| ~ less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f380,plain,
( spl0_46
<=> less_than(one,m) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f443,plain,
( ~ less_than(m,one)
| ~ spl0_19
| ~ spl0_46 ),
inference(resolution,[],[f382,f113]) ).
fof(f113,plain,
( ! [X0,X1] :
( ~ less_than(X1,X0)
| ~ less_than(X0,X1) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f382,plain,
( less_than(one,m)
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f469,plain,
( spl0_51
| ~ spl0_15
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f248,f191,f93,f466]) ).
fof(f466,plain,
( spl0_51
<=> less_than(predecessor(i),m) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f93,plain,
( spl0_15
<=> ! [X0] : less_than(predecessor(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f191,plain,
( spl0_27
<=> ! [X0] :
( ~ less_than(X0,i)
| less_than(X0,m) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f248,plain,
( less_than(predecessor(i),m)
| ~ spl0_15
| ~ spl0_27 ),
inference(resolution,[],[f192,f94]) ).
fof(f94,plain,
( ! [X0] : less_than(predecessor(X0),X0)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f192,plain,
( ! [X0] :
( ~ less_than(X0,i)
| less_than(X0,m) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f463,plain,
( spl0_50
| ~ spl0_15
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f235,f187,f93,f460]) ).
fof(f460,plain,
( spl0_50
<=> less_than(predecessor(i),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f187,plain,
( spl0_26
<=> ! [X0] :
( ~ less_than(X0,i)
| less_than(X0,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f235,plain,
( less_than(predecessor(i),n)
| ~ spl0_15
| ~ spl0_26 ),
inference(resolution,[],[f188,f94]) ).
fof(f188,plain,
( ! [X0] :
( ~ less_than(X0,i)
| less_than(X0,n) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f458,plain,
( ~ spl0_49
| spl0_14
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f203,f195,f88,f455]) ).
fof(f88,plain,
( spl0_14
<=> less_than(m,successor(n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f195,plain,
( spl0_28
<=> n = m ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f203,plain,
( ~ less_than(m,successor(m))
| spl0_14
| ~ spl0_28 ),
inference(superposition,[],[f90,f197]) ).
fof(f197,plain,
( n = m
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f90,plain,
( ~ less_than(m,successor(n))
| spl0_14 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f438,plain,
( ~ spl0_13
| spl0_24
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f204,f195,f171,f84]) ).
fof(f84,plain,
( spl0_13
<=> less_than(m,i) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f171,plain,
( spl0_24
<=> less_than(n,i) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f204,plain,
( ~ less_than(m,i)
| spl0_24
| ~ spl0_28 ),
inference(superposition,[],[f173,f197]) ).
fof(f173,plain,
( ~ less_than(n,i)
| spl0_24 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f419,plain,
( ~ spl0_13
| ~ spl0_5
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f118,f112,f47,f84]) ).
fof(f47,plain,
( spl0_5
<=> less_than(i,m) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f118,plain,
( ~ less_than(m,i)
| ~ spl0_5
| ~ spl0_19 ),
inference(resolution,[],[f113,f49]) ).
fof(f49,plain,
( less_than(i,m)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f413,plain,
( ~ spl0_29
| spl0_14
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f345,f334,f88,f199]) ).
fof(f199,plain,
( spl0_29
<=> less_than(m,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f334,plain,
( spl0_41
<=> ! [X0,X1] :
( ~ less_than(X0,X1)
| less_than(X0,successor(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f345,plain,
( ~ less_than(m,n)
| spl0_14
| ~ spl0_41 ),
inference(resolution,[],[f335,f90]) ).
fof(f335,plain,
( ! [X0,X1] :
( less_than(X0,successor(X1))
| ~ less_than(X0,X1) )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f412,plain,
( spl0_48
| ~ spl0_26
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f297,f216,f187,f403]) ).
fof(f403,plain,
( spl0_48
<=> less_than(one,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f216,plain,
( spl0_31
<=> less_than(one,i) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f297,plain,
( less_than(one,n)
| ~ spl0_26
| ~ spl0_31 ),
inference(resolution,[],[f218,f188]) ).
fof(f218,plain,
( less_than(one,i)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f406,plain,
( spl0_48
| ~ spl0_3
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f221,f212,f37,f403]) ).
fof(f37,plain,
( spl0_3
<=> less_than(i,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f212,plain,
( spl0_30
<=> i = one ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f221,plain,
( less_than(one,n)
| ~ spl0_3
| ~ spl0_30 ),
inference(superposition,[],[f39,f214]) ).
fof(f214,plain,
( i = one
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f39,plain,
( less_than(i,n)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f401,plain,
( ~ spl0_47
| spl0_2
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f220,f212,f32,f398]) ).
fof(f398,plain,
( spl0_47
<=> less_than(k,one) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f32,plain,
( spl0_2
<=> less_than(k,i) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f220,plain,
( ~ less_than(k,one)
| spl0_2
| ~ spl0_30 ),
inference(superposition,[],[f34,f214]) ).
fof(f34,plain,
( ~ less_than(k,i)
| spl0_2 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f383,plain,
( spl0_46
| ~ spl0_27
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f296,f216,f191,f380]) ).
fof(f296,plain,
( less_than(one,m)
| ~ spl0_27
| ~ spl0_31 ),
inference(resolution,[],[f218,f192]) ).
fof(f366,plain,
( spl0_45
| ~ spl0_22
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f148,f139,f135,f364]) ).
fof(f364,plain,
( spl0_45
<=> ! [X2,X0,X1] :
( less_than(X1,X0)
| X0 = X1
| ~ less_than(X2,X0)
| less_than(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f135,plain,
( spl0_22
<=> ! [X2,X0,X1] :
( ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| less_than(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f139,plain,
( spl0_23
<=> ! [X0,X1] :
( X0 = X1
| less_than(X1,X0)
| less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f148,plain,
( ! [X2,X0,X1] :
( less_than(X1,X0)
| X0 = X1
| ~ less_than(X2,X0)
| less_than(X2,X1) )
| ~ spl0_22
| ~ spl0_23 ),
inference(resolution,[],[f140,f136]) ).
fof(f136,plain,
( ! [X2,X0,X1] :
( ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| less_than(X0,X2) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f140,plain,
( ! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1)
| X0 = X1 )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f358,plain,
( spl0_44
| ~ spl0_18
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f131,f125,f105,f356]) ).
fof(f356,plain,
( spl0_44
<=> ! [X0,X1] :
( successor(X1) != X0
| predecessor(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f105,plain,
( spl0_18
<=> ! [X0] : successor(predecessor(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f125,plain,
( spl0_21
<=> ! [X0,X1] :
( X0 = X1
| successor(X0) != successor(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f131,plain,
( ! [X0,X1] :
( successor(X1) != X0
| predecessor(X0) = X1 )
| ~ spl0_18
| ~ spl0_21 ),
inference(superposition,[],[f126,f106]) ).
fof(f106,plain,
( ! [X0] : successor(predecessor(X0)) = X0
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f126,plain,
( ! [X0,X1] :
( successor(X0) != successor(X1)
| X0 = X1 )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f354,plain,
( spl0_43
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f128,f121,f101,f352]) ).
fof(f352,plain,
( spl0_43
<=> ! [X0,X1] :
( predecessor(X1) != X0
| successor(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f101,plain,
( spl0_17
<=> ! [X0] : predecessor(successor(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f121,plain,
( spl0_20
<=> ! [X0,X1] :
( X0 = X1
| predecessor(X0) != predecessor(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f128,plain,
( ! [X0,X1] :
( predecessor(X1) != X0
| successor(X0) = X1 )
| ~ spl0_17
| ~ spl0_20 ),
inference(superposition,[],[f122,f102]) ).
fof(f102,plain,
( ! [X0] : predecessor(successor(X0)) = X0
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f122,plain,
( ! [X0,X1] :
( predecessor(X0) != predecessor(X1)
| X0 = X1 )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f340,plain,
( spl0_42
| ~ spl0_15
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f143,f135,f93,f338]) ).
fof(f338,plain,
( spl0_42
<=> ! [X0,X1] :
( ~ less_than(X0,predecessor(X1))
| less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f143,plain,
( ! [X0,X1] :
( ~ less_than(X0,predecessor(X1))
| less_than(X0,X1) )
| ~ spl0_15
| ~ spl0_22 ),
inference(resolution,[],[f136,f94]) ).
fof(f336,plain,
( spl0_41
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f142,f135,f97,f334]) ).
fof(f142,plain,
( ! [X0,X1] :
( ~ less_than(X0,X1)
| less_than(X0,successor(X1)) )
| ~ spl0_16
| ~ spl0_22 ),
inference(resolution,[],[f136,f98]) ).
fof(f322,plain,
( spl0_40
| ~ spl0_12
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f156,f139,f80,f320]) ).
fof(f320,plain,
( spl0_40
<=> ! [X0] :
( less_than(a(predecessor(i)),a(X0))
| a(X0) = a(predecessor(i))
| less_than(X0,i)
| less_than(n,X0)
| ~ less_than(one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f80,plain,
( spl0_12
<=> ! [X0] :
( ~ less_than(one,X0)
| less_than(X0,i)
| less_than(n,X0)
| ~ less_than(a(X0),a(predecessor(i))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f156,plain,
( ! [X0] :
( less_than(a(predecessor(i)),a(X0))
| a(X0) = a(predecessor(i))
| less_than(X0,i)
| less_than(n,X0)
| ~ less_than(one,X0) )
| ~ spl0_12
| ~ spl0_23 ),
inference(resolution,[],[f140,f81]) ).
fof(f81,plain,
( ! [X0] :
( ~ less_than(a(X0),a(predecessor(i)))
| less_than(X0,i)
| less_than(n,X0)
| ~ less_than(one,X0) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f307,plain,
( spl0_39
| ~ spl0_28
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f285,f282,f195,f305]) ).
fof(f305,plain,
( spl0_39
<=> ! [X0] :
( ~ less_than(X0,successor(m))
| less_than(a(k),a(X0))
| a(k) = a(X0)
| less_than(X0,i) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f282,plain,
( spl0_36
<=> ! [X0] :
( less_than(a(k),a(X0))
| a(k) = a(X0)
| ~ less_than(X0,successor(n))
| less_than(X0,i) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f285,plain,
( ! [X0] :
( ~ less_than(X0,successor(m))
| less_than(a(k),a(X0))
| a(k) = a(X0)
| less_than(X0,i) )
| ~ spl0_28
| ~ spl0_36 ),
inference(forward_demodulation,[],[f283,f197]) ).
fof(f283,plain,
( ! [X0] :
( less_than(a(k),a(X0))
| a(k) = a(X0)
| ~ less_than(X0,successor(n))
| less_than(X0,i) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f295,plain,
( spl0_38
| ~ spl0_28
| ~ spl0_30
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f286,f282,f212,f195,f293]) ).
fof(f293,plain,
( spl0_38
<=> ! [X0] :
( less_than(X0,one)
| ~ less_than(X0,successor(m))
| less_than(a(k),a(X0))
| a(k) = a(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f286,plain,
( ! [X0] :
( less_than(X0,one)
| ~ less_than(X0,successor(m))
| less_than(a(k),a(X0))
| a(k) = a(X0) )
| ~ spl0_28
| ~ spl0_30
| ~ spl0_36 ),
inference(forward_demodulation,[],[f285,f214]) ).
fof(f291,plain,
( ~ spl0_37
| spl0_1
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f207,f195,f27,f288]) ).
fof(f288,plain,
( spl0_37
<=> less_than(m,k) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f27,plain,
( spl0_1
<=> less_than(n,k) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f207,plain,
( ~ less_than(m,k)
| spl0_1
| ~ spl0_28 ),
inference(superposition,[],[f29,f197]) ).
fof(f29,plain,
( ~ less_than(n,k)
| spl0_1 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f284,plain,
( spl0_36
| ~ spl0_10
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f157,f139,f71,f282]) ).
fof(f71,plain,
( spl0_10
<=> ! [X0] :
( less_than(X0,i)
| ~ less_than(X0,successor(n))
| ~ less_than(a(X0),a(k)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f157,plain,
( ! [X0] :
( less_than(a(k),a(X0))
| a(k) = a(X0)
| ~ less_than(X0,successor(n))
| less_than(X0,i) )
| ~ spl0_10
| ~ spl0_23 ),
inference(resolution,[],[f140,f72]) ).
fof(f72,plain,
( ! [X0] :
( ~ less_than(a(X0),a(k))
| ~ less_than(X0,successor(n))
| less_than(X0,i) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f274,plain,
( spl0_35
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f116,f112,f93,f272]) ).
fof(f272,plain,
( spl0_35
<=> ! [X0] : ~ less_than(X0,predecessor(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f116,plain,
( ! [X0] : ~ less_than(X0,predecessor(X0))
| ~ spl0_15
| ~ spl0_19 ),
inference(resolution,[],[f113,f94]) ).
fof(f270,plain,
( spl0_34
| ~ spl0_16
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f115,f112,f97,f268]) ).
fof(f268,plain,
( spl0_34
<=> ! [X0] : ~ less_than(successor(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f115,plain,
( ! [X0] : ~ less_than(successor(X0),X0)
| ~ spl0_16
| ~ spl0_19 ),
inference(resolution,[],[f113,f98]) ).
fof(f265,plain,
( spl0_33
| ~ spl0_9
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f109,f101,f67,f263]) ).
fof(f263,plain,
( spl0_33
<=> ! [X0] :
( ~ less_than(a(successor(X0)),a(X0))
| ~ less_than(one,successor(X0))
| ~ less_than(successor(X0),i) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f67,plain,
( spl0_9
<=> ! [X0] :
( ~ less_than(X0,i)
| ~ less_than(one,X0)
| ~ less_than(a(X0),a(predecessor(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f109,plain,
( ! [X0] :
( ~ less_than(a(successor(X0)),a(X0))
| ~ less_than(one,successor(X0))
| ~ less_than(successor(X0),i) )
| ~ spl0_9
| ~ spl0_17 ),
inference(superposition,[],[f68,f102]) ).
fof(f68,plain,
( ! [X0] :
( ~ less_than(a(X0),a(predecessor(X0)))
| ~ less_than(one,X0)
| ~ less_than(X0,i) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f258,plain,
( spl0_32
| ~ spl0_8
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f146,f135,f62,f256]) ).
fof(f256,plain,
( spl0_32
<=> ! [X0] :
( ~ less_than(X0,a(m))
| less_than(X0,a(k)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f62,plain,
( spl0_8
<=> less_than(a(m),a(k)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f146,plain,
( ! [X0] :
( ~ less_than(X0,a(m))
| less_than(X0,a(k)) )
| ~ spl0_8
| ~ spl0_22 ),
inference(resolution,[],[f136,f64]) ).
fof(f64,plain,
( less_than(a(m),a(k))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f219,plain,
( spl0_30
| spl0_31
| spl0_6
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f153,f139,f52,f216,f212]) ).
fof(f52,plain,
( spl0_6
<=> less_than(i,one) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f153,plain,
( less_than(one,i)
| i = one
| spl0_6
| ~ spl0_23 ),
inference(resolution,[],[f140,f54]) ).
fof(f54,plain,
( ~ less_than(i,one)
| spl0_6 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f202,plain,
( spl0_28
| spl0_29
| spl0_4
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f151,f139,f42,f199,f195]) ).
fof(f42,plain,
( spl0_4
<=> less_than(n,m) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f151,plain,
( less_than(m,n)
| n = m
| spl0_4
| ~ spl0_23 ),
inference(resolution,[],[f140,f44]) ).
fof(f44,plain,
( ~ less_than(n,m)
| spl0_4 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f193,plain,
( spl0_27
| ~ spl0_5
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f145,f135,f47,f191]) ).
fof(f145,plain,
( ! [X0] :
( ~ less_than(X0,i)
| less_than(X0,m) )
| ~ spl0_5
| ~ spl0_22 ),
inference(resolution,[],[f136,f49]) ).
fof(f189,plain,
( spl0_26
| ~ spl0_3
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f144,f135,f37,f187]) ).
fof(f144,plain,
( ! [X0] :
( ~ less_than(X0,i)
| less_than(X0,n) )
| ~ spl0_3
| ~ spl0_22 ),
inference(resolution,[],[f136,f39]) ).
fof(f183,plain,
( ~ spl0_25
| ~ spl0_8
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f119,f112,f62,f180]) ).
fof(f180,plain,
( spl0_25
<=> less_than(a(k),a(m)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f119,plain,
( ~ less_than(a(k),a(m))
| ~ spl0_8
| ~ spl0_19 ),
inference(resolution,[],[f113,f64]) ).
fof(f174,plain,
( ~ spl0_24
| ~ spl0_3
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f117,f112,f37,f171]) ).
fof(f117,plain,
( ~ less_than(n,i)
| ~ spl0_3
| ~ spl0_19 ),
inference(resolution,[],[f113,f39]) ).
fof(f141,plain,
spl0_23,
inference(avatar_split_clause,[],[f8,f139]) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
| less_than(X1,X0)
| less_than(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',all_related) ).
fof(f137,plain,
spl0_22,
inference(avatar_split_clause,[],[f7,f135]) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| less_than(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_than) ).
fof(f127,plain,
spl0_21,
inference(avatar_split_clause,[],[f4,f125]) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
| successor(X0) != successor(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined_successor) ).
fof(f123,plain,
spl0_20,
inference(avatar_split_clause,[],[f3,f121]) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
| predecessor(X0) != predecessor(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined_predecessor) ).
fof(f114,plain,
spl0_19,
inference(avatar_split_clause,[],[f10,f112]) ).
fof(f10,axiom,
! [X0,X1] :
( ~ less_than(X1,X0)
| ~ less_than(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',anti_symmetry_of_less_than) ).
fof(f107,plain,
spl0_18,
inference(avatar_split_clause,[],[f2,f105]) ).
fof(f2,axiom,
! [X0] : successor(predecessor(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_predecessor) ).
fof(f103,plain,
spl0_17,
inference(avatar_split_clause,[],[f1,f101]) ).
fof(f1,axiom,
! [X0] : predecessor(successor(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',predecessor_successor) ).
fof(f99,plain,
spl0_16,
inference(avatar_split_clause,[],[f6,f97]) ).
fof(f6,axiom,
! [X0] : less_than(X0,successor(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_than_successor) ).
fof(f95,plain,
spl0_15,
inference(avatar_split_clause,[],[f5,f93]) ).
fof(f5,axiom,
! [X0] : less_than(predecessor(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',predecessor_less_than) ).
fof(f91,plain,
( spl0_13
| ~ spl0_14
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f74,f71,f62,f88,f84]) ).
fof(f74,plain,
( ~ less_than(m,successor(n))
| less_than(m,i)
| ~ spl0_8
| ~ spl0_10 ),
inference(resolution,[],[f72,f64]) ).
fof(f82,plain,
spl0_12,
inference(avatar_split_clause,[],[f22,f80]) ).
fof(f22,axiom,
! [X0] :
( ~ less_than(one,X0)
| less_than(X0,i)
| less_than(n,X0)
| ~ less_than(a(X0),a(predecessor(i))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
fof(f78,plain,
spl0_11,
inference(avatar_split_clause,[],[f9,f76]) ).
fof(f76,plain,
( spl0_11
<=> ! [X0] : ~ less_than(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f9,axiom,
! [X0] : ~ less_than(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_not_less_than_x) ).
fof(f73,plain,
spl0_10,
inference(avatar_split_clause,[],[f23,f71]) ).
fof(f23,axiom,
! [X0] :
( less_than(X0,i)
| ~ less_than(X0,successor(n))
| ~ less_than(a(X0),a(k)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
fof(f69,plain,
spl0_9,
inference(avatar_split_clause,[],[f21,f67]) ).
fof(f21,axiom,
! [X0] :
( ~ less_than(X0,i)
| ~ less_than(one,X0)
| ~ less_than(a(X0),a(predecessor(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
fof(f65,plain,
spl0_8,
inference(avatar_split_clause,[],[f20,f62]) ).
fof(f20,axiom,
less_than(a(m),a(k)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
fof(f60,plain,
~ spl0_7,
inference(avatar_split_clause,[],[f19,f57]) ).
fof(f57,plain,
( spl0_7
<=> k = m ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f19,axiom,
k != m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
fof(f55,plain,
~ spl0_6,
inference(avatar_split_clause,[],[f18,f52]) ).
fof(f18,axiom,
~ less_than(i,one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
fof(f50,plain,
spl0_5,
inference(avatar_split_clause,[],[f17,f47]) ).
fof(f17,axiom,
less_than(i,m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
fof(f45,plain,
~ spl0_4,
inference(avatar_split_clause,[],[f16,f42]) ).
fof(f16,axiom,
~ less_than(n,m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f40,plain,
spl0_3,
inference(avatar_split_clause,[],[f15,f37]) ).
fof(f15,axiom,
less_than(i,n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f35,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f14,f32]) ).
fof(f14,axiom,
~ less_than(k,i),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f30,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f13,f27]) ).
fof(f13,axiom,
~ less_than(n,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SWV007-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n002.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri May 3 21:06:37 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.11/0.32 % (14450)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.33 % (14453)WARNING: value z3 for option sas not known
% 0.11/0.33 % (14454)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.33 % (14455)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.33 % (14452)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.33 % (14451)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.33 % (14457)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.33 % (14456)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.33 % (14453)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.33 TRYING [1]
% 0.11/0.33 TRYING [2]
% 0.11/0.34 TRYING [3]
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [4]
% 0.11/0.34 TRYING [2]
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [2]
% 0.11/0.34 TRYING [5]
% 0.11/0.34 TRYING [3]
% 0.11/0.34 TRYING [3]
% 0.11/0.34 TRYING [4]
% 0.11/0.34 % (14455)First to succeed.
% 0.11/0.34 % (14453)Also succeeded, but the first one will report.
% 0.11/0.34 TRYING [6]
% 0.11/0.34 TRYING [5]
% 0.11/0.35 % (14455)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14450"
% 0.11/0.35 % (14455)Refutation found. Thanks to Tanya!
% 0.11/0.35 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.35 % (14455)------------------------------
% 0.11/0.35 % (14455)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.35 % (14455)Termination reason: Refutation
% 0.11/0.35
% 0.11/0.35 % (14455)Memory used [KB]: 1012
% 0.11/0.35 % (14455)Time elapsed: 0.013 s
% 0.11/0.35 % (14455)Instructions burned: 19 (million)
% 0.11/0.35 % (14450)Success in time 0.027 s
%------------------------------------------------------------------------------