TSTP Solution File: NUM840+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM840+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n017.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 : Tue Apr 30 14:37:49 EDT 2024
% Result : Theorem 0.22s 0.48s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 97
% Syntax : Number of formulae : 318 ( 66 unt; 0 def)
% Number of atoms : 731 ( 170 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 718 ( 305 ~; 293 |; 25 &)
% ( 69 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 67 ( 65 usr; 62 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 469 ( 447 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f710,plain,
$false,
inference(avatar_sat_refutation,[],[f179,f183,f187,f191,f195,f199,f203,f207,f211,f215,f219,f223,f227,f231,f235,f239,f251,f255,f259,f263,f281,f285,f289,f293,f297,f301,f305,f309,f313,f339,f344,f348,f352,f356,f360,f364,f403,f407,f476,f518,f523,f528,f534,f549,f553,f605,f609,f624,f630,f636,f642,f648,f656,f660,f664,f668,f672,f676,f680,f685,f689,f703,f708,f709]) ).
fof(f709,plain,
( ~ spl4_17
| ~ spl4_10
| ~ spl4_43 ),
inference(avatar_split_clause,[],[f652,f525,f213,f248]) ).
fof(f248,plain,
( spl4_17
<=> less(vplus(vd328,vd330),vplus(vd329,vd330)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).
fof(f213,plain,
( spl4_10
<=> ! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
fof(f525,plain,
( spl4_43
<=> greater(vplus(vd328,vd330),vplus(vd329,vd330)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_43])]) ).
fof(f652,plain,
( ~ less(vplus(vd328,vd330),vplus(vd329,vd330))
| ~ spl4_10
| ~ spl4_43 ),
inference(resolution,[],[f526,f214]) ).
fof(f214,plain,
( ! [X0,X1] :
( ~ greater(X0,X1)
| ~ less(X0,X1) )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f526,plain,
( greater(vplus(vd328,vd330),vplus(vd329,vd330))
| ~ spl4_43 ),
inference(avatar_component_clause,[],[f525]) ).
fof(f708,plain,
( spl4_61
| ~ spl4_13
| ~ spl4_43 ),
inference(avatar_split_clause,[],[f651,f525,f225,f705]) ).
fof(f705,plain,
( spl4_61
<=> less(vplus(vd329,vd330),vplus(vd328,vd330)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_61])]) ).
fof(f225,plain,
( spl4_13
<=> ! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).
fof(f651,plain,
( less(vplus(vd329,vd330),vplus(vd328,vd330))
| ~ spl4_13
| ~ spl4_43 ),
inference(resolution,[],[f526,f226]) ).
fof(f226,plain,
( ! [X0,X1] :
( ~ greater(X0,X1)
| less(X1,X0) )
| ~ spl4_13 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f703,plain,
( spl4_60
| ~ spl4_15
| ~ spl4_43 ),
inference(avatar_split_clause,[],[f650,f525,f233,f700]) ).
fof(f700,plain,
( spl4_60
<=> geq(vplus(vd328,vd330),vplus(vd329,vd330)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_60])]) ).
fof(f233,plain,
( spl4_15
<=> ! [X0,X1] :
( geq(X1,X0)
| ~ greater(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).
fof(f650,plain,
( geq(vplus(vd328,vd330),vplus(vd329,vd330))
| ~ spl4_15
| ~ spl4_43 ),
inference(resolution,[],[f526,f234]) ).
fof(f234,plain,
( ! [X0,X1] :
( ~ greater(X1,X0)
| geq(X1,X0) )
| ~ spl4_15 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f689,plain,
( spl4_59
| ~ spl4_9
| ~ spl4_39 ),
inference(avatar_split_clause,[],[f455,f405,f209,f687]) ).
fof(f687,plain,
( spl4_59
<=> ! [X0,X1] : less(X0,vplus(v1,vplus(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_59])]) ).
fof(f209,plain,
( spl4_9
<=> ! [X2,X1] : less(X1,vplus(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
fof(f405,plain,
( spl4_39
<=> ! [X0,X1] : vplus(v1,vplus(X0,X1)) = vplus(X0,vplus(v1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_39])]) ).
fof(f455,plain,
( ! [X0,X1] : less(X0,vplus(v1,vplus(X0,X1)))
| ~ spl4_9
| ~ spl4_39 ),
inference(superposition,[],[f210,f406]) ).
fof(f406,plain,
( ! [X0,X1] : vplus(v1,vplus(X0,X1)) = vplus(X0,vplus(v1,X1))
| ~ spl4_39 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f210,plain,
( ! [X2,X1] : less(X1,vplus(X1,X2))
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f685,plain,
( spl4_58
| ~ spl4_13
| ~ spl4_31 ),
inference(avatar_split_clause,[],[f513,f336,f225,f682]) ).
fof(f682,plain,
( spl4_58
<=> less(vd329,vd328) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_58])]) ).
fof(f336,plain,
( spl4_31
<=> greater(vd328,vd329) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_31])]) ).
fof(f513,plain,
( less(vd329,vd328)
| ~ spl4_13
| ~ spl4_31 ),
inference(resolution,[],[f338,f226]) ).
fof(f338,plain,
( greater(vd328,vd329)
| ~ spl4_31 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f680,plain,
( spl4_57
| ~ spl4_7
| ~ spl4_39 ),
inference(avatar_split_clause,[],[f453,f405,f201,f678]) ).
fof(f678,plain,
( spl4_57
<=> ! [X0,X1] : greater(vplus(v1,vplus(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_57])]) ).
fof(f201,plain,
( spl4_7
<=> ! [X0,X1] : greater(vplus(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f453,plain,
( ! [X0,X1] : greater(vplus(v1,vplus(X0,X1)),X0)
| ~ spl4_7
| ~ spl4_39 ),
inference(superposition,[],[f202,f406]) ).
fof(f202,plain,
( ! [X0,X1] : greater(vplus(X0,X1),X0)
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f676,plain,
( spl4_56
| ~ spl4_9
| ~ spl4_39 ),
inference(avatar_split_clause,[],[f443,f405,f209,f674]) ).
fof(f674,plain,
( spl4_56
<=> ! [X0,X1] : less(v1,vplus(X0,vplus(v1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_56])]) ).
fof(f443,plain,
( ! [X0,X1] : less(v1,vplus(X0,vplus(v1,X1)))
| ~ spl4_9
| ~ spl4_39 ),
inference(superposition,[],[f210,f406]) ).
fof(f672,plain,
( spl4_55
| ~ spl4_7
| ~ spl4_39 ),
inference(avatar_split_clause,[],[f441,f405,f201,f670]) ).
fof(f670,plain,
( spl4_55
<=> ! [X0,X1] : greater(vplus(X0,vplus(v1,X1)),v1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_55])]) ).
fof(f441,plain,
( ! [X0,X1] : greater(vplus(X0,vplus(v1,X1)),v1)
| ~ spl4_7
| ~ spl4_39 ),
inference(superposition,[],[f202,f406]) ).
fof(f668,plain,
( spl4_54
| ~ spl4_6
| ~ spl4_38 ),
inference(avatar_split_clause,[],[f415,f401,f197,f666]) ).
fof(f666,plain,
( spl4_54
<=> ! [X2,X0,X1] : vplus(X0,vplus(X1,X2)) != X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_54])]) ).
fof(f197,plain,
( spl4_6
<=> ! [X0,X1] : vplus(X0,X1) != X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
fof(f401,plain,
( spl4_38
<=> ! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_38])]) ).
fof(f415,plain,
( ! [X2,X0,X1] : vplus(X0,vplus(X1,X2)) != X2
| ~ spl4_6
| ~ spl4_38 ),
inference(superposition,[],[f198,f402]) ).
fof(f402,plain,
( ! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2))
| ~ spl4_38 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f198,plain,
( ! [X0,X1] : vplus(X0,X1) != X1
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f664,plain,
( spl4_53
| ~ spl4_6
| ~ spl4_29 ),
inference(avatar_split_clause,[],[f326,f311,f197,f662]) ).
fof(f662,plain,
( spl4_53
<=> ! [X0] :
( vskolem2(X0) != X0
| v1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_53])]) ).
fof(f311,plain,
( spl4_29
<=> ! [X0] :
( vplus(v1,vskolem2(X0)) = X0
| v1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_29])]) ).
fof(f326,plain,
( ! [X0] :
( vskolem2(X0) != X0
| v1 = X0 )
| ~ spl4_6
| ~ spl4_29 ),
inference(superposition,[],[f198,f312]) ).
fof(f312,plain,
( ! [X0] :
( vplus(v1,vskolem2(X0)) = X0
| v1 = X0 )
| ~ spl4_29 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f660,plain,
( spl4_52
| ~ spl4_18
| ~ spl4_20 ),
inference(avatar_split_clause,[],[f276,f261,f253,f658]) ).
fof(f658,plain,
( spl4_52
<=> ! [X2,X0,X1] : vplus(X2,vplus(X0,X1)) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_52])]) ).
fof(f253,plain,
( spl4_18
<=> ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).
fof(f261,plain,
( spl4_20
<=> ! [X2,X0,X3] : vplus(vplus(X0,X2),X3) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).
fof(f276,plain,
( ! [X2,X0,X1] : vplus(X2,vplus(X0,X1)) != X0
| ~ spl4_18
| ~ spl4_20 ),
inference(superposition,[],[f262,f254]) ).
fof(f254,plain,
( ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0)
| ~ spl4_18 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f262,plain,
( ! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0
| ~ spl4_20 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f656,plain,
( spl4_51
| ~ spl4_18
| ~ spl4_20 ),
inference(avatar_split_clause,[],[f274,f261,f253,f654]) ).
fof(f654,plain,
( spl4_51
<=> ! [X2,X0,X1] : vplus(vplus(X1,X0),X2) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_51])]) ).
fof(f274,plain,
( ! [X2,X0,X1] : vplus(vplus(X1,X0),X2) != X0
| ~ spl4_18
| ~ spl4_20 ),
inference(superposition,[],[f262,f254]) ).
fof(f648,plain,
( ~ spl4_31
| ~ spl4_36
| spl4_43 ),
inference(avatar_split_clause,[],[f643,f525,f358,f336]) ).
fof(f358,plain,
( spl4_36
<=> ! [X2,X0,X1] :
( greater(vplus(X0,X2),vplus(X1,X2))
| ~ greater(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_36])]) ).
fof(f643,plain,
( ~ greater(vd328,vd329)
| ~ spl4_36
| spl4_43 ),
inference(resolution,[],[f527,f359]) ).
fof(f359,plain,
( ! [X2,X0,X1] :
( greater(vplus(X0,X2),vplus(X1,X2))
| ~ greater(X0,X1) )
| ~ spl4_36 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f527,plain,
( ~ greater(vplus(vd328,vd330),vplus(vd329,vd330))
| spl4_43 ),
inference(avatar_component_clause,[],[f525]) ).
fof(f642,plain,
( ~ spl4_2
| ~ spl4_50 ),
inference(avatar_contradiction_clause,[],[f637]) ).
fof(f637,plain,
( $false
| ~ spl4_2
| ~ spl4_50 ),
inference(resolution,[],[f635,f182]) ).
fof(f182,plain,
( ! [X1] : ~ greater(X1,X1)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f181,plain,
( spl4_2
<=> ! [X1] : ~ greater(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f635,plain,
( greater(vplus(vd328,vd330),vplus(vd328,vd330))
| ~ spl4_50 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f633,plain,
( spl4_50
<=> greater(vplus(vd328,vd330),vplus(vd328,vd330)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_50])]) ).
fof(f636,plain,
( spl4_50
| ~ spl4_30
| ~ spl4_49 ),
inference(avatar_split_clause,[],[f631,f627,f332,f633]) ).
fof(f332,plain,
( spl4_30
<=> vd328 = vd329 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_30])]) ).
fof(f627,plain,
( spl4_49
<=> greater(vplus(vd329,vd330),vplus(vd328,vd330)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_49])]) ).
fof(f631,plain,
( greater(vplus(vd328,vd330),vplus(vd328,vd330))
| ~ spl4_30
| ~ spl4_49 ),
inference(forward_demodulation,[],[f629,f334]) ).
fof(f334,plain,
( vd328 = vd329
| ~ spl4_30 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f629,plain,
( greater(vplus(vd329,vd330),vplus(vd328,vd330))
| ~ spl4_49 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f630,plain,
( spl4_49
| ~ spl4_14
| ~ spl4_17 ),
inference(avatar_split_clause,[],[f265,f248,f229,f627]) ).
fof(f229,plain,
( spl4_14
<=> ! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
fof(f265,plain,
( greater(vplus(vd329,vd330),vplus(vd328,vd330))
| ~ spl4_14
| ~ spl4_17 ),
inference(resolution,[],[f250,f230]) ).
fof(f230,plain,
( ! [X0,X1] :
( ~ less(X0,X1)
| greater(X1,X0) )
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f250,plain,
( less(vplus(vd328,vd330),vplus(vd329,vd330))
| ~ spl4_17 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f624,plain,
( spl4_48
| ~ spl4_16
| ~ spl4_17 ),
inference(avatar_split_clause,[],[f264,f248,f237,f621]) ).
fof(f621,plain,
( spl4_48
<=> leq(vplus(vd328,vd330),vplus(vd329,vd330)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_48])]) ).
fof(f237,plain,
( spl4_16
<=> ! [X0,X1] :
( leq(X1,X0)
| ~ less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).
fof(f264,plain,
( leq(vplus(vd328,vd330),vplus(vd329,vd330))
| ~ spl4_16
| ~ spl4_17 ),
inference(resolution,[],[f250,f238]) ).
fof(f238,plain,
( ! [X0,X1] :
( ~ less(X1,X0)
| leq(X1,X0) )
| ~ spl4_16 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f609,plain,
( spl4_47
| ~ spl4_9
| ~ spl4_29 ),
inference(avatar_split_clause,[],[f329,f311,f209,f607]) ).
fof(f607,plain,
( spl4_47
<=> ! [X0] :
( less(v1,X0)
| v1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_47])]) ).
fof(f329,plain,
( ! [X0] :
( less(v1,X0)
| v1 = X0 )
| ~ spl4_9
| ~ spl4_29 ),
inference(superposition,[],[f210,f312]) ).
fof(f605,plain,
( spl4_46
| ~ spl4_7
| ~ spl4_29 ),
inference(avatar_split_clause,[],[f327,f311,f201,f603]) ).
fof(f603,plain,
( spl4_46
<=> ! [X0] :
( greater(X0,v1)
| v1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_46])]) ).
fof(f327,plain,
( ! [X0] :
( greater(X0,v1)
| v1 = X0 )
| ~ spl4_7
| ~ spl4_29 ),
inference(superposition,[],[f202,f312]) ).
fof(f553,plain,
( spl4_45
| ~ spl4_7
| ~ spl4_18 ),
inference(avatar_split_clause,[],[f268,f253,f201,f551]) ).
fof(f551,plain,
( spl4_45
<=> ! [X0,X1] : greater(vplus(X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_45])]) ).
fof(f268,plain,
( ! [X0,X1] : greater(vplus(X1,X0),X0)
| ~ spl4_7
| ~ spl4_18 ),
inference(superposition,[],[f202,f254]) ).
fof(f549,plain,
( spl4_44
| ~ spl4_9
| ~ spl4_18 ),
inference(avatar_split_clause,[],[f266,f253,f209,f547]) ).
fof(f547,plain,
( spl4_44
<=> ! [X0,X1] : less(X0,vplus(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_44])]) ).
fof(f266,plain,
( ! [X0,X1] : less(X0,vplus(X1,X0))
| ~ spl4_9
| ~ spl4_18 ),
inference(superposition,[],[f210,f254]) ).
fof(f534,plain,
( ~ spl4_30
| spl4_32 ),
inference(avatar_contradiction_clause,[],[f533]) ).
fof(f533,plain,
( $false
| ~ spl4_30
| spl4_32 ),
inference(trivial_inequality_removal,[],[f530]) ).
fof(f530,plain,
( vplus(vd328,vd330) != vplus(vd328,vd330)
| ~ spl4_30
| spl4_32 ),
inference(superposition,[],[f343,f334]) ).
fof(f343,plain,
( vplus(vd328,vd330) != vplus(vd329,vd330)
| spl4_32 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f341,plain,
( spl4_32
<=> vplus(vd328,vd330) = vplus(vd329,vd330) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_32])]) ).
fof(f528,plain,
( ~ spl4_43
| spl4_31 ),
inference(avatar_split_clause,[],[f113,f336,f525]) ).
fof(f113,plain,
( greater(vd328,vd329)
| ~ greater(vplus(vd328,vd330),vplus(vd329,vd330)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
( greater(vd328,vd329)
| ~ greater(vplus(vd328,vd330),vplus(vd329,vd330)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
( greater(vplus(vd328,vd330),vplus(vd329,vd330))
=> greater(vd328,vd329) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conjunct1(204), 0), 0)') ).
fof(f523,plain,
( spl4_42
| ~ spl4_15
| ~ spl4_31 ),
inference(avatar_split_clause,[],[f512,f336,f233,f520]) ).
fof(f520,plain,
( spl4_42
<=> geq(vd328,vd329) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_42])]) ).
fof(f512,plain,
( geq(vd328,vd329)
| ~ spl4_15
| ~ spl4_31 ),
inference(resolution,[],[f338,f234]) ).
fof(f518,plain,
( spl4_41
| ~ spl4_9
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f246,f237,f209,f516]) ).
fof(f516,plain,
( spl4_41
<=> ! [X0,X1] : leq(X0,vplus(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_41])]) ).
fof(f246,plain,
( ! [X0,X1] : leq(X0,vplus(X0,X1))
| ~ spl4_9
| ~ spl4_16 ),
inference(resolution,[],[f238,f210]) ).
fof(f476,plain,
spl4_40,
inference(avatar_split_clause,[],[f130,f474]) ).
fof(f474,plain,
( spl4_40
<=> ! [X0,X1] :
( vplus(X0,sK0(X0,X1)) = X1
| vplus(X1,sK1(X0,X1)) = X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_40])]) ).
fof(f130,plain,
! [X0,X1] :
( vplus(X0,sK0(X0,X1)) = X1
| vplus(X1,sK1(X0,X1)) = X0
| X0 = X1 ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( vplus(X0,sK0(X0,X1)) = X1
| vplus(X1,sK1(X0,X1)) = X0
| X0 = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f57,f96,f95]) ).
fof(f95,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
=> vplus(X0,sK0(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0,X1] :
( ? [X3] : vplus(X1,X3) = X0
=> vplus(X1,sK1(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
| ? [X3] : vplus(X1,X3) = X0
| X0 = X1 ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X34,X35] :
( ? [X37] : vplus(X34,X37) = X35
| ? [X36] : vplus(X35,X36) = X34
| X34 = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof(f407,plain,
spl4_39,
inference(avatar_split_clause,[],[f162,f405]) ).
fof(f162,plain,
! [X0,X1] : vplus(v1,vplus(X0,X1)) = vplus(X0,vplus(v1,X1)),
inference(definition_unfolding,[],[f122,f116,f116]) ).
fof(f116,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X47] : vplus(v1,X47) = vsucc(X47),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof(f122,plain,
! [X0,X1] : vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( vsucc(X0) = vplus(X0,v1)
& vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X51,X52] :
( vplus(X51,v1) = vsucc(X51)
& vplus(X51,vsucc(X52)) = vsucc(vplus(X51,X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
fof(f403,plain,
spl4_38,
inference(avatar_split_clause,[],[f149,f401]) ).
fof(f149,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X48,X49,X50] : vplus(vplus(X48,X49),X50) = vplus(X48,vplus(X49,X50)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(f364,plain,
spl4_37,
inference(avatar_split_clause,[],[f152,f362]) ).
fof(f362,plain,
( spl4_37
<=> ! [X2,X0,X1] :
( less(vplus(X0,X2),vplus(X1,X2))
| ~ less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_37])]) ).
fof(f152,plain,
! [X2,X0,X1] :
( less(vplus(X0,X2),vplus(X1,X2))
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( less(vplus(X0,X2),vplus(X1,X2))
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( less(X0,X1)
=> less(vplus(X0,X2),vplus(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
fof(f360,plain,
spl4_36,
inference(avatar_split_clause,[],[f151,f358]) ).
fof(f151,plain,
! [X2,X0,X1] :
( greater(vplus(X0,X2),vplus(X1,X2))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( greater(vplus(X0,X2),vplus(X1,X2))
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( greater(X0,X1)
=> greater(vplus(X0,X2),vplus(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
fof(f356,plain,
spl4_35,
inference(avatar_split_clause,[],[f147,f354]) ).
fof(f354,plain,
( spl4_35
<=> ! [X0,X1] :
( vplus(X1,sK3(X0,X1)) = X0
| ~ less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_35])]) ).
fof(f147,plain,
! [X0,X1] :
( vplus(X1,sK3(X0,X1)) = X0
| ~ less(X1,X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( vplus(X1,sK3(X0,X1)) = X0
| ~ less(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f107,f108]) ).
fof(f108,plain,
! [X0,X1] :
( ? [X3] : vplus(X1,X3) = X0
=> vplus(X1,sK3(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X3] : vplus(X1,X3) = X0
| ~ less(X1,X0) ) ),
inference(rectify,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X2] : vplus(X1,X2) = X0
| ~ less(X1,X0) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( less(X1,X0)
<=> ? [X2] : vplus(X1,X2) = X0 ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X28,X29] :
( less(X29,X28)
<=> ? [X30] : vplus(X29,X30) = X28 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof(f352,plain,
spl4_34,
inference(avatar_split_clause,[],[f145,f350]) ).
fof(f350,plain,
( spl4_34
<=> ! [X0,X1] :
( vplus(X0,sK2(X0,X1)) = X1
| ~ greater(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_34])]) ).
fof(f145,plain,
! [X0,X1] :
( vplus(X0,sK2(X0,X1)) = X1
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( vplus(X0,sK2(X0,X1)) = X1
| ~ greater(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f103,f104]) ).
fof(f104,plain,
! [X0,X1] :
( ? [X3] : vplus(X0,X3) = X1
=> vplus(X0,sK2(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : vplus(X0,X2) = X1
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : vplus(X0,X2) = X1 ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X31,X32] :
( greater(X32,X31)
<=> ? [X33] : vplus(X31,X33) = X32 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f348,plain,
spl4_33,
inference(avatar_split_clause,[],[f133,f346]) ).
fof(f346,plain,
( spl4_33
<=> ! [X2,X0,X1] :
( vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_33])]) ).
fof(f133,plain,
! [X2,X0,X1] :
( vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ! [X2] : vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( X0 != X1
=> ! [X2] : vplus(X2,X0) != vplus(X2,X1) ),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X38,X39] :
( X38 != X39
=> ! [X40] : vplus(X40,X38) != vplus(X40,X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof(f344,plain,
( ~ spl4_32
| spl4_30 ),
inference(avatar_split_clause,[],[f112,f332,f341]) ).
fof(f112,plain,
( vd328 = vd329
| vplus(vd328,vd330) != vplus(vd329,vd330) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( vd328 = vd329
| vplus(vd328,vd330) != vplus(vd329,vd330) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
( vplus(vd328,vd330) = vplus(vd329,vd330)
=> vd328 = vd329 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conjunct1(conjunct2(204)), 0), 0)') ).
fof(f339,plain,
( spl4_30
| spl4_31
| spl4_1
| ~ spl4_21 ),
inference(avatar_split_clause,[],[f314,f279,f176,f336,f332]) ).
fof(f176,plain,
( spl4_1
<=> less(vd328,vd329) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f279,plain,
( spl4_21
<=> ! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).
fof(f314,plain,
( greater(vd328,vd329)
| vd328 = vd329
| spl4_1
| ~ spl4_21 ),
inference(resolution,[],[f280,f178]) ).
fof(f178,plain,
( ~ less(vd328,vd329)
| spl4_1 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f280,plain,
( ! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 )
| ~ spl4_21 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f313,plain,
spl4_29,
inference(avatar_split_clause,[],[f159,f311]) ).
fof(f159,plain,
! [X0] :
( vplus(v1,vskolem2(X0)) = X0
| v1 = X0 ),
inference(definition_unfolding,[],[f117,f116]) ).
fof(f117,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( v1 != X0
=> vsucc(vskolem2(X0)) = X0 ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X53] :
( v1 != X53
=> vsucc(vskolem2(X53)) = X53 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof(f309,plain,
spl4_28,
inference(avatar_split_clause,[],[f156,f307]) ).
fof(f307,plain,
( spl4_28
<=> ! [X2,X0,X1] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ leq(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_28])]) ).
fof(f156,plain,
! [X2,X0,X1] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ leq(X1,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ( ( ~ less(X0,X1)
| ~ leq(X1,X2) )
& ( ~ leq(X0,X1)
| ~ less(X1,X2) ) ) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( ( less(X0,X1)
& leq(X1,X2) )
| ( leq(X0,X1)
& less(X1,X2) ) )
=> less(X0,X2) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X8,X9,X10] :
( ( ( less(X8,X9)
& leq(X9,X10) )
| ( leq(X8,X9)
& less(X9,X10) ) )
=> less(X8,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(177), 0), 0)') ).
fof(f305,plain,
( spl4_27
| ~ spl4_7
| ~ spl4_15 ),
inference(avatar_split_clause,[],[f245,f233,f201,f303]) ).
fof(f303,plain,
( spl4_27
<=> ! [X0,X1] : geq(vplus(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_27])]) ).
fof(f245,plain,
( ! [X0,X1] : geq(vplus(X0,X1),X0)
| ~ spl4_7
| ~ spl4_15 ),
inference(resolution,[],[f234,f202]) ).
fof(f301,plain,
spl4_26,
inference(avatar_split_clause,[],[f155,f299]) ).
fof(f299,plain,
( spl4_26
<=> ! [X2,X0,X1] :
( less(X0,X2)
| ~ leq(X0,X1)
| ~ less(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_26])]) ).
fof(f155,plain,
! [X2,X0,X1] :
( less(X0,X2)
| ~ leq(X0,X1)
| ~ less(X1,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f297,plain,
spl4_25,
inference(avatar_split_clause,[],[f154,f295]) ).
fof(f295,plain,
( spl4_25
<=> ! [X2,X0,X1] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ less(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_25])]) ).
fof(f154,plain,
! [X2,X0,X1] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ less(X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ less(X1,X2) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ less(X1,X2) ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( less(X0,X1)
& less(X1,X2) )
=> less(X0,X2) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X11,X12,X13] :
( ( less(X11,X12)
& less(X12,X13) )
=> less(X11,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
fof(f293,plain,
spl4_24,
inference(avatar_split_clause,[],[f153,f291]) ).
fof(f291,plain,
( spl4_24
<=> ! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_24])]) ).
fof(f153,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( leq(X0,X1)
& leq(X1,X2) )
=> leq(X0,X2) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X5,X6,X7] :
( ( leq(X5,X6)
& leq(X6,X7) )
=> leq(X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(184, 0), 0)') ).
fof(f289,plain,
spl4_23,
inference(avatar_split_clause,[],[f142,f287]) ).
fof(f287,plain,
( spl4_23
<=> ! [X0,X1] :
( X0 = X1
| less(X1,X0)
| ~ leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_23])]) ).
fof(f142,plain,
! [X0,X1] :
( X0 = X1
| less(X1,X0)
| ~ leq(X1,X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1] :
( ( leq(X1,X0)
| ( X0 != X1
& ~ less(X1,X0) ) )
& ( X0 = X1
| less(X1,X0)
| ~ leq(X1,X0) ) ),
inference(flattening,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ( leq(X1,X0)
| ( X0 != X1
& ~ less(X1,X0) ) )
& ( X0 = X1
| less(X1,X0)
| ~ leq(X1,X0) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( leq(X1,X0)
<=> ( X0 = X1
| less(X1,X0) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X18,X19] :
( leq(X19,X18)
<=> ( X18 = X19
| less(X19,X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
fof(f285,plain,
spl4_22,
inference(avatar_split_clause,[],[f139,f283]) ).
fof(f283,plain,
( spl4_22
<=> ! [X0,X1] :
( X0 = X1
| greater(X1,X0)
| ~ geq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).
fof(f139,plain,
! [X0,X1] :
( X0 = X1
| greater(X1,X0)
| ~ geq(X1,X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ( geq(X1,X0)
| ( X0 != X1
& ~ greater(X1,X0) ) )
& ( X0 = X1
| greater(X1,X0)
| ~ geq(X1,X0) ) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( geq(X1,X0)
| ( X0 != X1
& ~ greater(X1,X0) ) )
& ( X0 = X1
| greater(X1,X0)
| ~ geq(X1,X0) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( geq(X1,X0)
<=> ( X0 = X1
| greater(X1,X0) ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X20,X21] :
( geq(X21,X20)
<=> ( X20 = X21
| greater(X21,X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
fof(f281,plain,
spl4_21,
inference(avatar_split_clause,[],[f129,f279]) ).
fof(f129,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X26,X27] :
( less(X26,X27)
| greater(X26,X27)
| X26 = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof(f263,plain,
spl4_20,
inference(avatar_split_clause,[],[f169,f261]) ).
fof(f169,plain,
! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0,
inference(equality_resolution,[],[f131]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( vplus(X0,X2) != X1
| vplus(X1,X3) != X0 ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| ! [X3] : vplus(X1,X3) != X0 ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| ~ ? [X3] : vplus(X1,X3) = X0 ),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X34,X35] :
( ~ ? [X37] : vplus(X34,X37) = X35
| ~ ? [X36] : vplus(X35,X36) = X34 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
fof(f259,plain,
( spl4_19
| ~ spl4_7
| ~ spl4_10 ),
inference(avatar_split_clause,[],[f240,f213,f201,f257]) ).
fof(f257,plain,
( spl4_19
<=> ! [X0,X1] : ~ less(vplus(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).
fof(f240,plain,
( ! [X0,X1] : ~ less(vplus(X0,X1),X0)
| ~ spl4_7
| ~ spl4_10 ),
inference(resolution,[],[f214,f202]) ).
fof(f255,plain,
spl4_18,
inference(avatar_split_clause,[],[f120,f253]) ).
fof(f120,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X43,X44] : vplus(X44,X43) = vplus(X43,X44),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f251,plain,
spl4_17,
inference(avatar_split_clause,[],[f111,f248]) ).
fof(f111,plain,
less(vplus(vd328,vd330),vplus(vd329,vd330)),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
less(vplus(vd328,vd330),vplus(vd329,vd330)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(conjunct2(conjunct2(204))), 335, 0)') ).
fof(f239,plain,
spl4_16,
inference(avatar_split_clause,[],[f143,f237]) ).
fof(f143,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ less(X1,X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f235,plain,
spl4_15,
inference(avatar_split_clause,[],[f140,f233]) ).
fof(f140,plain,
! [X0,X1] :
( geq(X1,X0)
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f231,plain,
spl4_14,
inference(avatar_split_clause,[],[f137,f229]) ).
fof(f137,plain,
! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( less(X0,X1)
=> greater(X1,X0) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X22,X23] :
( less(X22,X23)
=> greater(X23,X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof(f227,plain,
spl4_13,
inference(avatar_split_clause,[],[f136,f225]) ).
fof(f136,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( greater(X0,X1)
=> less(X1,X0) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X24,X25] :
( greater(X24,X25)
=> less(X25,X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof(f223,plain,
spl4_12,
inference(avatar_split_clause,[],[f135,f221]) ).
fof(f221,plain,
( spl4_12
<=> ! [X0,X1] :
( geq(X1,X0)
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).
fof(f135,plain,
! [X0,X1] :
( geq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( geq(X1,X0)
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( leq(X0,X1)
=> geq(X1,X0) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X14,X15] :
( leq(X14,X15)
=> geq(X15,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
fof(f219,plain,
spl4_11,
inference(avatar_split_clause,[],[f134,f217]) ).
fof(f217,plain,
( spl4_11
<=> ! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
fof(f134,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( geq(X0,X1)
=> leq(X1,X0) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X16,X17] :
( geq(X16,X17)
=> leq(X17,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
fof(f215,plain,
spl4_10,
inference(avatar_split_clause,[],[f128,f213]) ).
fof(f128,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X26,X27] :
( ~ less(X26,X27)
| ~ greater(X26,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof(f211,plain,
spl4_9,
inference(avatar_split_clause,[],[f173,f209]) ).
fof(f173,plain,
! [X2,X1] : less(X1,vplus(X1,X2)),
inference(equality_resolution,[],[f148]) ).
fof(f148,plain,
! [X2,X0,X1] :
( less(X1,X0)
| vplus(X1,X2) != X0 ),
inference(cnf_transformation,[],[f109]) ).
fof(f207,plain,
spl4_8,
inference(avatar_split_clause,[],[f167,f205]) ).
fof(f205,plain,
( spl4_8
<=> ! [X2,X1] : vplus(X1,X2) != X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f167,plain,
! [X2,X1] : vplus(X1,X2) != X1,
inference(equality_resolution,[],[f126]) ).
fof(f126,plain,
! [X2,X0,X1] :
( vplus(X1,X2) != X0
| X0 != X1 ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ! [X2] : vplus(X1,X2) != X0
| X0 != X1 ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X1,X2) = X0
| X0 != X1 ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X34,X35] :
( ~ ? [X36] : vplus(X35,X36) = X34
| X34 != X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof(f203,plain,
spl4_7,
inference(avatar_split_clause,[],[f119,f201]) ).
fof(f119,plain,
! [X0,X1] : greater(vplus(X0,X1),X0),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] : greater(vplus(X0,X1),X0),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X3,X4] : greater(vplus(X3,X4),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof(f199,plain,
spl4_6,
inference(avatar_split_clause,[],[f118,f197]) ).
fof(f118,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X41,X42] : vplus(X41,X42) != X42,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof(f195,plain,
spl4_5,
inference(avatar_split_clause,[],[f171,f193]) ).
fof(f193,plain,
( spl4_5
<=> ! [X1] : leq(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
fof(f171,plain,
! [X1] : leq(X1,X1),
inference(equality_resolution,[],[f144]) ).
fof(f144,plain,
! [X0,X1] :
( leq(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f101]) ).
fof(f191,plain,
spl4_4,
inference(avatar_split_clause,[],[f170,f189]) ).
fof(f189,plain,
( spl4_4
<=> ! [X1] : geq(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
fof(f170,plain,
! [X1] : geq(X1,X1),
inference(equality_resolution,[],[f141]) ).
fof(f141,plain,
! [X0,X1] :
( geq(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f99]) ).
fof(f187,plain,
spl4_3,
inference(avatar_split_clause,[],[f166,f185]) ).
fof(f185,plain,
( spl4_3
<=> ! [X1] : ~ less(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
fof(f166,plain,
! [X1] : ~ less(X1,X1),
inference(equality_resolution,[],[f125]) ).
fof(f125,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X26,X27] :
( ~ less(X26,X27)
| X26 != X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
fof(f183,plain,
spl4_2,
inference(avatar_split_clause,[],[f165,f181]) ).
fof(f165,plain,
! [X1] : ~ greater(X1,X1),
inference(equality_resolution,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 != X1 ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X26,X27] :
( ~ greater(X26,X27)
| X26 != X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
fof(f179,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f110,f176]) ).
fof(f110,plain,
~ less(vd328,vd329),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
~ less(vd328,vd329),
inference(flattening,[],[f2]) ).
fof(f2,negated_conjecture,
~ less(vd328,vd329),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
less(vd328,vd329),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(conjunct2(conjunct2(204))), 336, 0)') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.17 % Problem : NUM840+1 : TPTP v8.1.2. Released v4.1.0.
% 0.15/0.18 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.40 % Computer : n017.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8042.1875MB
% 0.15/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon Apr 29 23:18:03 EDT 2024
% 0.15/0.40 % CPUTime :
% 0.15/0.41 % (20274)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.44 % (20280)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)
% 0.15/0.44 % (20278)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.44 % (20281)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)
% 0.15/0.44 % (20279)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)
% 0.15/0.44 TRYING [1]
% 0.15/0.44 TRYING [2]
% 0.15/0.45 TRYING [3]
% 0.15/0.46 TRYING [4]
% 0.22/0.47 % (20279)First to succeed.
% 0.22/0.48 % (20275)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.48 % (20279)Refutation found. Thanks to Tanya!
% 0.22/0.48 % SZS status Theorem for theBenchmark
% 0.22/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.49 % (20279)------------------------------
% 0.22/0.49 % (20279)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.49 % (20279)Termination reason: Refutation
% 0.22/0.49
% 0.22/0.49 % (20279)Memory used [KB]: 1135
% 0.22/0.49 % (20279)Time elapsed: 0.043 s
% 0.22/0.49 % (20279)Instructions burned: 35 (million)
% 0.22/0.49 % (20279)------------------------------
% 0.22/0.49 % (20279)------------------------------
% 0.22/0.49 % (20274)Success in time 0.073 s
%------------------------------------------------------------------------------