TSTP Solution File: KLE002+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE002+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.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 13:11:24 EDT 2024
% Result : Theorem 0.21s 0.46s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 57
% Syntax : Number of formulae : 177 ( 41 unt; 0 def)
% Number of atoms : 400 ( 108 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 400 ( 177 ~; 170 |; 5 &)
% ( 44 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 46 ( 44 usr; 44 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 259 ( 253 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1625,plain,
$false,
inference(avatar_sat_refutation,[],[f40,f45,f49,f53,f57,f61,f65,f69,f73,f81,f85,f95,f100,f104,f139,f143,f210,f215,f219,f230,f235,f251,f275,f279,f296,f300,f304,f308,f312,f628,f709,f757,f761,f895,f899,f1027,f1031,f1035,f1039,f1449,f1453,f1574,f1578,f1613]) ).
fof(f1613,plain,
( spl3_2
| ~ spl3_43 ),
inference(avatar_contradiction_clause,[],[f1603]) ).
fof(f1603,plain,
( $false
| spl3_2
| ~ spl3_43 ),
inference(resolution,[],[f1577,f44]) ).
fof(f44,plain,
( ~ leq(multiplication(sK0,sK2),multiplication(sK1,sK2))
| spl3_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f42,plain,
( spl3_2
<=> leq(multiplication(sK0,sK2),multiplication(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f1577,plain,
( ! [X0] : leq(multiplication(sK0,X0),multiplication(sK1,X0))
| ~ spl3_43 ),
inference(avatar_component_clause,[],[f1576]) ).
fof(f1576,plain,
( spl3_43
<=> ! [X0] : leq(multiplication(sK0,X0),multiplication(sK1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_43])]) ).
fof(f1578,plain,
( spl3_43
| ~ spl3_13
| ~ spl3_35 ),
inference(avatar_split_clause,[],[f980,f897,f97,f1576]) ).
fof(f97,plain,
( spl3_13
<=> sK1 = addition(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f897,plain,
( spl3_35
<=> ! [X2,X0,X1] :
( multiplication(X2,X1) != multiplication(addition(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_35])]) ).
fof(f980,plain,
( ! [X0] : leq(multiplication(sK0,X0),multiplication(sK1,X0))
| ~ spl3_13
| ~ spl3_35 ),
inference(trivial_inequality_removal,[],[f973]) ).
fof(f973,plain,
( ! [X0] :
( multiplication(sK1,X0) != multiplication(sK1,X0)
| leq(multiplication(sK0,X0),multiplication(sK1,X0)) )
| ~ spl3_13
| ~ spl3_35 ),
inference(superposition,[],[f898,f99]) ).
fof(f99,plain,
( sK1 = addition(sK0,sK1)
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f898,plain,
( ! [X2,X0,X1] :
( multiplication(X2,X1) != multiplication(addition(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) )
| ~ spl3_35 ),
inference(avatar_component_clause,[],[f897]) ).
fof(f1574,plain,
( spl3_42
| ~ spl3_13
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f926,f893,f97,f1572]) ).
fof(f1572,plain,
( spl3_42
<=> ! [X0] : leq(multiplication(X0,sK0),multiplication(X0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_42])]) ).
fof(f893,plain,
( spl3_34
<=> ! [X2,X0,X1] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).
fof(f926,plain,
( ! [X0] : leq(multiplication(X0,sK0),multiplication(X0,sK1))
| ~ spl3_13
| ~ spl3_34 ),
inference(trivial_inequality_removal,[],[f918]) ).
fof(f918,plain,
( ! [X0] :
( multiplication(X0,sK1) != multiplication(X0,sK1)
| leq(multiplication(X0,sK0),multiplication(X0,sK1)) )
| ~ spl3_13
| ~ spl3_34 ),
inference(superposition,[],[f894,f99]) ).
fof(f894,plain,
( ! [X2,X0,X1] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) )
| ~ spl3_34 ),
inference(avatar_component_clause,[],[f893]) ).
fof(f1453,plain,
( spl3_41
| ~ spl3_9
| ~ spl3_30 ),
inference(avatar_split_clause,[],[f949,f626,f71,f1451]) ).
fof(f1451,plain,
( spl3_41
<=> ! [X0] : leq(sK0,addition(X0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_41])]) ).
fof(f71,plain,
( spl3_9
<=> ! [X0,X1] : addition(X0,X1) = addition(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f626,plain,
( spl3_30
<=> ! [X0] : leq(sK0,addition(sK1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).
fof(f949,plain,
( ! [X0] : leq(sK0,addition(X0,sK1))
| ~ spl3_9
| ~ spl3_30 ),
inference(superposition,[],[f627,f72]) ).
fof(f72,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X1,X0)
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f627,plain,
( ! [X0] : leq(sK0,addition(sK1,X0))
| ~ spl3_30 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f1449,plain,
( spl3_40
| ~ spl3_14
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f166,f137,f102,f1447]) ).
fof(f1447,plain,
( spl3_40
<=> ! [X0,X3,X2,X1] : addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))) = multiplication(X0,multiplication(X1,addition(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_40])]) ).
fof(f102,plain,
( spl3_14
<=> ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f137,plain,
( spl3_15
<=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
fof(f166,plain,
( ! [X2,X3,X0,X1] : addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))) = multiplication(X0,multiplication(X1,addition(X2,X3)))
| ~ spl3_14
| ~ spl3_15 ),
inference(forward_demodulation,[],[f165,f103]) ).
fof(f103,plain,
( ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2)
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f165,plain,
( ! [X2,X3,X0,X1] : multiplication(multiplication(X0,X1),addition(X2,X3)) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3)))
| ~ spl3_14
| ~ spl3_15 ),
inference(forward_demodulation,[],[f147,f103]) ).
fof(f147,plain,
( ! [X2,X3,X0,X1] : multiplication(multiplication(X0,X1),addition(X2,X3)) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,X1),X3))
| ~ spl3_14
| ~ spl3_15 ),
inference(superposition,[],[f138,f103]) ).
fof(f138,plain,
( ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2))
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f1039,plain,
( spl3_39
| ~ spl3_12
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f190,f141,f93,f1037]) ).
fof(f1037,plain,
( spl3_39
<=> ! [X0,X3,X2,X1] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_39])]) ).
fof(f93,plain,
( spl3_12
<=> ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f141,plain,
( spl3_16
<=> ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f190,plain,
( ! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3)
| ~ spl3_12
| ~ spl3_16 ),
inference(superposition,[],[f94,f142]) ).
fof(f142,plain,
( ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2))
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f94,plain,
( ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0)
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f1035,plain,
( spl3_38
| ~ spl3_14
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f182,f141,f102,f1033]) ).
fof(f1033,plain,
( spl3_38
<=> ! [X0,X3,X2,X1] : multiplication(addition(X3,multiplication(X0,X1)),X2) = addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_38])]) ).
fof(f182,plain,
( ! [X2,X3,X0,X1] : multiplication(addition(X3,multiplication(X0,X1)),X2) = addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2)))
| ~ spl3_14
| ~ spl3_16 ),
inference(superposition,[],[f142,f103]) ).
fof(f1031,plain,
( spl3_37
| ~ spl3_14
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f177,f141,f102,f1029]) ).
fof(f1029,plain,
( spl3_37
<=> ! [X0,X3,X2,X1] : multiplication(addition(multiplication(X0,X1),X3),X2) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).
fof(f177,plain,
( ! [X2,X3,X0,X1] : multiplication(addition(multiplication(X0,X1),X3),X2) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2))
| ~ spl3_14
| ~ spl3_16 ),
inference(superposition,[],[f142,f103]) ).
fof(f1027,plain,
( spl3_36
| ~ spl3_12
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f158,f137,f93,f1025]) ).
fof(f1025,plain,
( spl3_36
<=> ! [X0,X3,X2,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).
fof(f158,plain,
( ! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3)
| ~ spl3_12
| ~ spl3_15 ),
inference(superposition,[],[f94,f138]) ).
fof(f899,plain,
( spl3_35
| ~ spl3_11
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f191,f141,f83,f897]) ).
fof(f83,plain,
( spl3_11
<=> ! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
fof(f191,plain,
( ! [X2,X0,X1] :
( multiplication(X2,X1) != multiplication(addition(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) )
| ~ spl3_11
| ~ spl3_16 ),
inference(superposition,[],[f84,f142]) ).
fof(f84,plain,
( ! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) )
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f895,plain,
( spl3_34
| ~ spl3_11
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f159,f137,f83,f893]) ).
fof(f159,plain,
( ! [X2,X0,X1] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) )
| ~ spl3_11
| ~ spl3_15 ),
inference(superposition,[],[f84,f138]) ).
fof(f761,plain,
( spl3_33
| ~ spl3_9
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f186,f141,f71,f759]) ).
fof(f759,plain,
( spl3_33
<=> ! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).
fof(f186,plain,
( ! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1))
| ~ spl3_9
| ~ spl3_16 ),
inference(superposition,[],[f142,f72]) ).
fof(f757,plain,
( spl3_32
| ~ spl3_9
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f155,f137,f71,f755]) ).
fof(f755,plain,
( spl3_32
<=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).
fof(f155,plain,
( ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1))
| ~ spl3_9
| ~ spl3_15 ),
inference(superposition,[],[f138,f72]) ).
fof(f709,plain,
( spl3_31
| ~ spl3_11
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f116,f93,f83,f707]) ).
fof(f707,plain,
( spl3_31
<=> ! [X2,X0,X1] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).
fof(f116,plain,
( ! [X2,X0,X1] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) )
| ~ spl3_11
| ~ spl3_12 ),
inference(superposition,[],[f84,f94]) ).
fof(f628,plain,
( spl3_30
| ~ spl3_11
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f290,f213,f83,f626]) ).
fof(f213,plain,
( spl3_18
<=> ! [X0] : addition(sK1,X0) = addition(sK0,addition(sK1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
fof(f290,plain,
( ! [X0] : leq(sK0,addition(sK1,X0))
| ~ spl3_11
| ~ spl3_18 ),
inference(trivial_inequality_removal,[],[f289]) ).
fof(f289,plain,
( ! [X0] :
( addition(sK1,X0) != addition(sK1,X0)
| leq(sK0,addition(sK1,X0)) )
| ~ spl3_11
| ~ spl3_18 ),
inference(superposition,[],[f84,f214]) ).
fof(f214,plain,
( ! [X0] : addition(sK1,X0) = addition(sK0,addition(sK1,X0))
| ~ spl3_18 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f312,plain,
( spl3_29
| ~ spl3_7
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f183,f141,f63,f310]) ).
fof(f310,plain,
( spl3_29
<=> ! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).
fof(f63,plain,
( spl3_7
<=> ! [X0] : multiplication(one,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f183,plain,
( ! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0)
| ~ spl3_7
| ~ spl3_16 ),
inference(superposition,[],[f142,f64]) ).
fof(f64,plain,
( ! [X0] : multiplication(one,X0) = X0
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f308,plain,
( spl3_28
| ~ spl3_7
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f178,f141,f63,f306]) ).
fof(f306,plain,
( spl3_28
<=> ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).
fof(f178,plain,
( ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0))
| ~ spl3_7
| ~ spl3_16 ),
inference(superposition,[],[f142,f64]) ).
fof(f304,plain,
( spl3_27
| ~ spl3_6
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f150,f137,f59,f302]) ).
fof(f302,plain,
( spl3_27
<=> ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).
fof(f59,plain,
( spl3_6
<=> ! [X0] : multiplication(X0,one) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f150,plain,
( ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0)
| ~ spl3_6
| ~ spl3_15 ),
inference(superposition,[],[f138,f60]) ).
fof(f60,plain,
( ! [X0] : multiplication(X0,one) = X0
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f300,plain,
( spl3_26
| ~ spl3_6
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f145,f137,f59,f298]) ).
fof(f298,plain,
( spl3_26
<=> ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
fof(f145,plain,
( ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1))
| ~ spl3_6
| ~ spl3_15 ),
inference(superposition,[],[f138,f60]) ).
fof(f296,plain,
( spl3_25
| ~ spl3_9
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f112,f93,f71,f294]) ).
fof(f294,plain,
( spl3_25
<=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
fof(f112,plain,
( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1))
| ~ spl3_9
| ~ spl3_12 ),
inference(superposition,[],[f94,f72]) ).
fof(f279,plain,
( spl3_24
| ~ spl3_8
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f111,f93,f67,f277]) ).
fof(f277,plain,
( spl3_24
<=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
fof(f67,plain,
( spl3_8
<=> ! [X0] : addition(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f111,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1)))
| ~ spl3_8
| ~ spl3_12 ),
inference(superposition,[],[f94,f68]) ).
fof(f68,plain,
( ! [X0] : addition(X0,X0) = X0
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f275,plain,
( spl3_23
| ~ spl3_9
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f107,f93,f71,f273]) ).
fof(f273,plain,
( spl3_23
<=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
fof(f107,plain,
( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2)
| ~ spl3_9
| ~ spl3_12 ),
inference(superposition,[],[f94,f72]) ).
fof(f251,plain,
( spl3_22
| ~ spl3_8
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f106,f93,f67,f249]) ).
fof(f249,plain,
( spl3_22
<=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
fof(f106,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1))
| ~ spl3_8
| ~ spl3_12 ),
inference(superposition,[],[f94,f68]) ).
fof(f235,plain,
( spl3_21
| ~ spl3_9
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f89,f83,f71,f233]) ).
fof(f233,plain,
( spl3_21
<=> ! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
fof(f89,plain,
( ! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) )
| ~ spl3_9
| ~ spl3_11 ),
inference(superposition,[],[f84,f72]) ).
fof(f230,plain,
( spl3_20
| ~ spl3_5
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f87,f83,f55,f228]) ).
fof(f228,plain,
( spl3_20
<=> ! [X0] :
( zero != X0
| leq(X0,zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
fof(f55,plain,
( spl3_5
<=> ! [X0] : addition(X0,zero) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f87,plain,
( ! [X0] :
( zero != X0
| leq(X0,zero) )
| ~ spl3_5
| ~ spl3_11 ),
inference(superposition,[],[f84,f56]) ).
fof(f56,plain,
( ! [X0] : addition(X0,zero) = X0
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f219,plain,
( spl3_19
| ~ spl3_5
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f74,f71,f55,f217]) ).
fof(f217,plain,
( spl3_19
<=> ! [X0] : addition(zero,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
fof(f74,plain,
( ! [X0] : addition(zero,X0) = X0
| ~ spl3_5
| ~ spl3_9 ),
inference(superposition,[],[f72,f56]) ).
fof(f215,plain,
( spl3_18
| ~ spl3_12
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f204,f97,f93,f213]) ).
fof(f204,plain,
( ! [X0] : addition(sK1,X0) = addition(sK0,addition(sK1,X0))
| ~ spl3_12
| ~ spl3_13 ),
inference(superposition,[],[f94,f99]) ).
fof(f210,plain,
( spl3_17
| ~ spl3_8
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f91,f83,f67,f208]) ).
fof(f208,plain,
( spl3_17
<=> ! [X0] : leq(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
fof(f91,plain,
( ! [X0] : leq(X0,X0)
| ~ spl3_8
| ~ spl3_11 ),
inference(trivial_inequality_removal,[],[f88]) ).
fof(f88,plain,
( ! [X0] :
( X0 != X0
| leq(X0,X0) )
| ~ spl3_8
| ~ spl3_11 ),
inference(superposition,[],[f84,f68]) ).
fof(f143,plain,
spl3_16,
inference(avatar_split_clause,[],[f35,f141]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f139,plain,
spl3_15,
inference(avatar_split_clause,[],[f34,f137]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f104,plain,
spl3_14,
inference(avatar_split_clause,[],[f33,f102]) ).
fof(f33,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f100,plain,
( spl3_13
| ~ spl3_1
| ~ spl3_10 ),
inference(avatar_split_clause,[],[f86,f79,f37,f97]) ).
fof(f37,plain,
( spl3_1
<=> leq(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f79,plain,
( spl3_10
<=> ! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f86,plain,
( sK1 = addition(sK0,sK1)
| ~ spl3_1
| ~ spl3_10 ),
inference(resolution,[],[f80,f39]) ).
fof(f39,plain,
( leq(sK0,sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f80,plain,
( ! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f95,plain,
spl3_12,
inference(avatar_split_clause,[],[f32,f93]) ).
fof(f32,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f85,plain,
spl3_11,
inference(avatar_split_clause,[],[f31,f83]) ).
fof(f31,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f81,plain,
spl3_10,
inference(avatar_split_clause,[],[f30,f79]) ).
fof(f30,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f73,plain,
spl3_9,
inference(avatar_split_clause,[],[f29,f71]) ).
fof(f29,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f69,plain,
spl3_8,
inference(avatar_split_clause,[],[f28,f67]) ).
fof(f28,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f65,plain,
spl3_7,
inference(avatar_split_clause,[],[f27,f63]) ).
fof(f27,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f61,plain,
spl3_6,
inference(avatar_split_clause,[],[f26,f59]) ).
fof(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f57,plain,
spl3_5,
inference(avatar_split_clause,[],[f25,f55]) ).
fof(f25,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f53,plain,
spl3_4,
inference(avatar_split_clause,[],[f24,f51]) ).
fof(f51,plain,
( spl3_4
<=> ! [X0] : zero = multiplication(zero,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f24,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f49,plain,
spl3_3,
inference(avatar_split_clause,[],[f23,f47]) ).
fof(f47,plain,
( spl3_3
<=> ! [X0] : zero = multiplication(X0,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f23,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(X0,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
fof(f45,plain,
~ spl3_2,
inference(avatar_split_clause,[],[f22,f42]) ).
fof(f22,plain,
~ leq(multiplication(sK0,sK2),multiplication(sK1,sK2)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
( ~ leq(multiplication(sK0,sK2),multiplication(sK1,sK2))
& leq(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f18]) ).
fof(f18,plain,
( ? [X0,X1,X2] :
( ~ leq(multiplication(X0,X2),multiplication(X1,X2))
& leq(X0,X1) )
=> ( ~ leq(multiplication(sK0,sK2),multiplication(sK1,sK2))
& leq(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(X0,X2),multiplication(X1,X2))
& leq(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
~ ! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ),
inference(rectify,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X3,X4,X5] :
( leq(X3,X4)
=> leq(multiplication(X3,X5),multiplication(X4,X5)) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X3,X4,X5] :
( leq(X3,X4)
=> leq(multiplication(X3,X5),multiplication(X4,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f40,plain,
spl3_1,
inference(avatar_split_clause,[],[f21,f37]) ).
fof(f21,plain,
leq(sK0,sK1),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE002+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 05:23:29 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (8819)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (8822)WARNING: value z3 for option sas not known
% 0.14/0.38 % (8820)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (8821)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (8822)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)
% 0.14/0.38 % (8824)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)
% 0.14/0.38 % (8826)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)
% 0.14/0.38 % (8825)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)
% 0.14/0.38 % (8823)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 TRYING [4]
% 0.21/0.39 TRYING [3]
% 0.21/0.42 TRYING [5]
% 0.21/0.42 TRYING [4]
% 0.21/0.42 TRYING [1]
% 0.21/0.42 TRYING [2]
% 0.21/0.43 TRYING [3]
% 0.21/0.44 TRYING [4]
% 0.21/0.45 % (8824)First to succeed.
% 0.21/0.46 % (8824)Refutation found. Thanks to Tanya!
% 0.21/0.46 % SZS status Theorem for theBenchmark
% 0.21/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.46 % (8824)------------------------------
% 0.21/0.46 % (8824)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.46 % (8824)Termination reason: Refutation
% 0.21/0.46
% 0.21/0.46 % (8824)Memory used [KB]: 1791
% 0.21/0.46 % (8824)Time elapsed: 0.077 s
% 0.21/0.46 % (8824)Instructions burned: 122 (million)
% 0.21/0.46 % (8824)------------------------------
% 0.21/0.46 % (8824)------------------------------
% 0.21/0.46 % (8819)Success in time 0.096 s
%------------------------------------------------------------------------------