TSTP Solution File: KLE009+4 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE009+4 : 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 : n013.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 07:16:48 EDT 2024
% Result : Theorem 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 93
% Syntax : Number of formulae : 338 ( 51 unt; 0 def)
% Number of atoms : 1031 ( 246 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1260 ( 567 ~; 565 |; 34 &)
% ( 80 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 77 ( 75 usr; 73 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 381 ( 370 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1333,plain,
$false,
inference(avatar_sat_refutation,[],[f79,f84,f88,f92,f96,f100,f104,f108,f112,f116,f120,f124,f130,f138,f142,f146,f150,f166,f170,f182,f193,f198,f202,f206,f241,f245,f309,f313,f323,f327,f348,f352,f356,f377,f381,f386,f407,f411,f415,f422,f426,f431,f435,f439,f443,f447,f451,f476,f494,f517,f522,f526,f531,f535,f540,f544,f548,f552,f556,f560,f883,f988,f1032,f1036,f1170,f1172,f1195,f1199,f1203,f1323,f1327,f1331,f1332]) ).
fof(f1332,plain,
( ~ spl3_62
| ~ spl3_1
| ~ spl3_2
| ~ spl3_6
| ~ spl3_13
| spl3_22
| ~ spl3_26
| ~ spl3_27
| ~ spl3_47
| ~ spl3_54 ),
inference(avatar_split_clause,[],[f704,f529,f445,f243,f239,f190,f128,f98,f81,f76,f880]) ).
fof(f880,plain,
( spl3_62
<=> leq(one,one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_62])]) ).
fof(f76,plain,
( spl3_1
<=> test(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f81,plain,
( spl3_2
<=> test(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f98,plain,
( spl3_6
<=> ! [X0] : multiplication(X0,one) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f128,plain,
( spl3_13
<=> ! [X0,X1] : addition(X0,X1) = addition(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f190,plain,
( spl3_22
<=> leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1))))),one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
fof(f239,plain,
( spl3_26
<=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
fof(f243,plain,
( spl3_27
<=> ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).
fof(f445,plain,
( spl3_47
<=> ! [X0] :
( one = addition(X0,c(X0))
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_47])]) ).
fof(f529,plain,
( spl3_54
<=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_54])]) ).
fof(f704,plain,
( ~ leq(one,one)
| ~ spl3_1
| ~ spl3_2
| ~ spl3_6
| ~ spl3_13
| spl3_22
| ~ spl3_26
| ~ spl3_27
| ~ spl3_47
| ~ spl3_54 ),
inference(forward_demodulation,[],[f703,f479]) ).
fof(f479,plain,
( one = addition(sK0,c(sK0))
| ~ spl3_2
| ~ spl3_47 ),
inference(resolution,[],[f446,f83]) ).
fof(f83,plain,
( test(sK0)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f446,plain,
( ! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) )
| ~ spl3_47 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f703,plain,
( ~ leq(addition(sK0,c(sK0)),one)
| ~ spl3_1
| ~ spl3_6
| ~ spl3_13
| spl3_22
| ~ spl3_26
| ~ spl3_27
| ~ spl3_47
| ~ spl3_54 ),
inference(forward_demodulation,[],[f702,f99]) ).
fof(f99,plain,
( ! [X0] : multiplication(X0,one) = X0
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f702,plain,
( ~ leq(multiplication(addition(sK0,c(sK0)),one),one)
| ~ spl3_1
| ~ spl3_13
| spl3_22
| ~ spl3_26
| ~ spl3_27
| ~ spl3_47
| ~ spl3_54 ),
inference(forward_demodulation,[],[f701,f480]) ).
fof(f480,plain,
( one = addition(sK1,c(sK1))
| ~ spl3_1
| ~ spl3_47 ),
inference(resolution,[],[f446,f78]) ).
fof(f78,plain,
( test(sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f701,plain,
( ~ leq(multiplication(addition(sK0,c(sK0)),addition(sK1,c(sK1))),one)
| ~ spl3_13
| spl3_22
| ~ spl3_26
| ~ spl3_27
| ~ spl3_54 ),
inference(forward_demodulation,[],[f700,f244]) ).
fof(f244,plain,
( ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2))
| ~ spl3_27 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f700,plain,
( ~ leq(addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),addition(sK1,c(sK1)))),one)
| ~ spl3_13
| spl3_22
| ~ spl3_26
| ~ spl3_54 ),
inference(forward_demodulation,[],[f699,f129]) ).
fof(f129,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X1,X0)
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f699,plain,
( ~ leq(addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),addition(c(sK1),sK1))),one)
| spl3_22
| ~ spl3_26
| ~ spl3_54 ),
inference(forward_demodulation,[],[f665,f610]) ).
fof(f610,plain,
( ! [X2,X3,X0,X1] : addition(X3,multiplication(X0,addition(X1,X2))) = addition(multiplication(X0,X2),addition(X3,multiplication(X0,X1)))
| ~ spl3_26
| ~ spl3_54 ),
inference(superposition,[],[f530,f240]) ).
fof(f240,plain,
( ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2))
| ~ spl3_26 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f530,plain,
( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1))
| ~ spl3_54 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f665,plain,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),c(sK1)))),one)
| spl3_22
| ~ spl3_54 ),
inference(superposition,[],[f192,f530]) ).
fof(f192,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1))))),one)
| spl3_22 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f1331,plain,
( spl3_72
| ~ spl3_25
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f284,f243,f204,f1329]) ).
fof(f1329,plain,
( spl3_72
<=> ! [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_72])]) ).
fof(f204,plain,
( spl3_25
<=> ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
fof(f284,plain,
( ! [X2,X3,X0,X1] : multiplication(addition(X3,multiplication(X0,X1)),X2) = addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2)))
| ~ spl3_25
| ~ spl3_27 ),
inference(superposition,[],[f244,f205]) ).
fof(f205,plain,
( ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2)
| ~ spl3_25 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f1327,plain,
( spl3_71
| ~ spl3_25
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f279,f243,f204,f1325]) ).
fof(f1325,plain,
( spl3_71
<=> ! [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_71])]) ).
fof(f279,plain,
( ! [X2,X3,X0,X1] : multiplication(addition(multiplication(X0,X1),X3),X2) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2))
| ~ spl3_25
| ~ spl3_27 ),
inference(superposition,[],[f244,f205]) ).
fof(f1323,plain,
( spl3_70
| ~ spl3_24
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f260,f239,f200,f1321]) ).
fof(f1321,plain,
( spl3_70
<=> ! [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_70])]) ).
fof(f200,plain,
( spl3_24
<=> ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
fof(f260,plain,
( ! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3)
| ~ spl3_24
| ~ spl3_26 ),
inference(superposition,[],[f201,f240]) ).
fof(f201,plain,
( ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0)
| ~ spl3_24 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f1203,plain,
( spl3_69
| ~ spl3_10
| ~ spl3_29 ),
inference(avatar_split_clause,[],[f319,f311,f114,f1201]) ).
fof(f1201,plain,
( spl3_69
<=> ! [X0,X1] :
( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X0)
| zero = c(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_69])]) ).
fof(f114,plain,
( spl3_10
<=> ! [X0] :
( zero = c(X0)
| test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f311,plain,
( spl3_29
<=> ! [X0,X1] :
( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).
fof(f319,plain,
( ! [X0,X1] :
( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X0)
| zero = c(X1) )
| ~ spl3_10
| ~ spl3_29 ),
inference(resolution,[],[f312,f115]) ).
fof(f115,plain,
( ! [X0] :
( test(X0)
| zero = c(X0) )
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f312,plain,
( ! [X0,X1] :
( ~ test(X1)
| c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X0) )
| ~ spl3_29 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f1199,plain,
( spl3_68
| ~ spl3_10
| ~ spl3_28 ),
inference(avatar_split_clause,[],[f316,f307,f114,f1197]) ).
fof(f1197,plain,
( spl3_68
<=> ! [X0,X1] :
( multiplication(c(X0),c(X1)) = c(addition(X0,X1))
| ~ test(X0)
| zero = c(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_68])]) ).
fof(f307,plain,
( spl3_28
<=> ! [X0,X1] :
( multiplication(c(X0),c(X1)) = c(addition(X0,X1))
| ~ test(X1)
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).
fof(f316,plain,
( ! [X0,X1] :
( multiplication(c(X0),c(X1)) = c(addition(X0,X1))
| ~ test(X0)
| zero = c(X1) )
| ~ spl3_10
| ~ spl3_28 ),
inference(resolution,[],[f308,f115]) ).
fof(f308,plain,
( ! [X0,X1] :
( ~ test(X1)
| multiplication(c(X0),c(X1)) = c(addition(X0,X1))
| ~ test(X0) )
| ~ spl3_28 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f1195,plain,
( spl3_67
| ~ spl3_17
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f293,f243,f148,f1193]) ).
fof(f1193,plain,
( spl3_67
<=> ! [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_67])]) ).
fof(f148,plain,
( spl3_17
<=> ! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
fof(f293,plain,
( ! [X2,X0,X1] :
( multiplication(X2,X1) != multiplication(addition(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) )
| ~ spl3_17
| ~ spl3_27 ),
inference(superposition,[],[f149,f244]) ).
fof(f149,plain,
( ! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) )
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f1172,plain,
( ~ spl3_18
| spl3_62 ),
inference(avatar_contradiction_clause,[],[f1171]) ).
fof(f1171,plain,
( $false
| ~ spl3_18
| spl3_62 ),
inference(resolution,[],[f882,f165]) ).
fof(f165,plain,
( ! [X0] : leq(X0,X0)
| ~ spl3_18 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f164,plain,
( spl3_18
<=> ! [X0] : leq(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
fof(f882,plain,
( ~ leq(one,one)
| spl3_62 ),
inference(avatar_component_clause,[],[f880]) ).
fof(f1170,plain,
( spl3_66
| ~ spl3_17
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f261,f239,f148,f1168]) ).
fof(f1168,plain,
( spl3_66
<=> ! [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_66])]) ).
fof(f261,plain,
( ! [X2,X0,X1] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) )
| ~ spl3_17
| ~ spl3_26 ),
inference(superposition,[],[f149,f240]) ).
fof(f1036,plain,
( spl3_65
| ~ spl3_13
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f288,f243,f128,f1034]) ).
fof(f1034,plain,
( spl3_65
<=> ! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_65])]) ).
fof(f288,plain,
( ! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1))
| ~ spl3_13
| ~ spl3_27 ),
inference(superposition,[],[f244,f129]) ).
fof(f1032,plain,
( spl3_64
| ~ spl3_13
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f257,f239,f128,f1030]) ).
fof(f1030,plain,
( spl3_64
<=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_64])]) ).
fof(f257,plain,
( ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1))
| ~ spl3_13
| ~ spl3_26 ),
inference(superposition,[],[f240,f129]) ).
fof(f988,plain,
( spl3_63
| ~ spl3_17
| ~ spl3_24 ),
inference(avatar_split_clause,[],[f218,f200,f148,f986]) ).
fof(f986,plain,
( spl3_63
<=> ! [X2,X0,X1] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_63])]) ).
fof(f218,plain,
( ! [X2,X0,X1] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) )
| ~ spl3_17
| ~ spl3_24 ),
inference(superposition,[],[f149,f201]) ).
fof(f883,plain,
( ~ spl3_62
| ~ spl3_1
| ~ spl3_2
| ~ spl3_6
| ~ spl3_13
| spl3_23
| ~ spl3_26
| ~ spl3_27
| ~ spl3_47
| ~ spl3_54 ),
inference(avatar_split_clause,[],[f698,f529,f445,f243,f239,f195,f128,f98,f81,f76,f880]) ).
fof(f195,plain,
( spl3_23
<=> leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
fof(f698,plain,
( ~ leq(one,one)
| ~ spl3_1
| ~ spl3_2
| ~ spl3_6
| ~ spl3_13
| spl3_23
| ~ spl3_26
| ~ spl3_27
| ~ spl3_47
| ~ spl3_54 ),
inference(forward_demodulation,[],[f697,f479]) ).
fof(f697,plain,
( ~ leq(one,addition(sK0,c(sK0)))
| ~ spl3_1
| ~ spl3_6
| ~ spl3_13
| spl3_23
| ~ spl3_26
| ~ spl3_27
| ~ spl3_47
| ~ spl3_54 ),
inference(forward_demodulation,[],[f696,f99]) ).
fof(f696,plain,
( ~ leq(one,multiplication(addition(sK0,c(sK0)),one))
| ~ spl3_1
| ~ spl3_13
| spl3_23
| ~ spl3_26
| ~ spl3_27
| ~ spl3_47
| ~ spl3_54 ),
inference(forward_demodulation,[],[f695,f480]) ).
fof(f695,plain,
( ~ leq(one,multiplication(addition(sK0,c(sK0)),addition(sK1,c(sK1))))
| ~ spl3_13
| spl3_23
| ~ spl3_26
| ~ spl3_27
| ~ spl3_54 ),
inference(forward_demodulation,[],[f694,f244]) ).
fof(f694,plain,
( ~ leq(one,addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),addition(sK1,c(sK1)))))
| ~ spl3_13
| spl3_23
| ~ spl3_26
| ~ spl3_54 ),
inference(forward_demodulation,[],[f693,f129]) ).
fof(f693,plain,
( ~ leq(one,addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),addition(c(sK1),sK1))))
| spl3_23
| ~ spl3_26
| ~ spl3_54 ),
inference(forward_demodulation,[],[f664,f610]) ).
fof(f664,plain,
( ~ leq(one,addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),c(sK1)))))
| spl3_23
| ~ spl3_54 ),
inference(superposition,[],[f197,f530]) ).
fof(f197,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1))))))
| spl3_23 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f560,plain,
( spl3_61
| ~ spl3_6
| ~ spl3_7
| ~ spl3_30 ),
inference(avatar_split_clause,[],[f344,f321,f102,f98,f558]) ).
fof(f558,plain,
( spl3_61
<=> ! [X0] :
( zero != X0
| one != addition(X0,one)
| complement(one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_61])]) ).
fof(f102,plain,
( spl3_7
<=> ! [X0] : multiplication(one,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f321,plain,
( spl3_30
<=> ! [X0,X1] :
( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).
fof(f344,plain,
( ! [X0] :
( zero != X0
| one != addition(X0,one)
| complement(one,X0) )
| ~ spl3_6
| ~ spl3_7
| ~ spl3_30 ),
inference(duplicate_literal_removal,[],[f343]) ).
fof(f343,plain,
( ! [X0] :
( zero != X0
| zero != X0
| one != addition(X0,one)
| complement(one,X0) )
| ~ spl3_6
| ~ spl3_7
| ~ spl3_30 ),
inference(forward_demodulation,[],[f332,f99]) ).
fof(f332,plain,
( ! [X0] :
( zero != X0
| one != addition(X0,one)
| complement(one,X0)
| zero != multiplication(X0,one) )
| ~ spl3_7
| ~ spl3_30 ),
inference(superposition,[],[f322,f103]) ).
fof(f103,plain,
( ! [X0] : multiplication(one,X0) = X0
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f322,plain,
( ! [X0,X1] :
( zero != multiplication(X1,X0)
| addition(X0,X1) != one
| complement(X1,X0)
| zero != multiplication(X0,X1) )
| ~ spl3_30 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f556,plain,
( spl3_60
| ~ spl3_6
| ~ spl3_7
| ~ spl3_30 ),
inference(avatar_split_clause,[],[f339,f321,f102,f98,f554]) ).
fof(f554,plain,
( spl3_60
<=> ! [X0] :
( zero != X0
| one != addition(one,X0)
| complement(X0,one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_60])]) ).
fof(f339,plain,
( ! [X0] :
( zero != X0
| one != addition(one,X0)
| complement(X0,one) )
| ~ spl3_6
| ~ spl3_7
| ~ spl3_30 ),
inference(duplicate_literal_removal,[],[f338]) ).
fof(f338,plain,
( ! [X0] :
( zero != X0
| zero != X0
| one != addition(one,X0)
| complement(X0,one) )
| ~ spl3_6
| ~ spl3_7
| ~ spl3_30 ),
inference(forward_demodulation,[],[f329,f103]) ).
fof(f329,plain,
( ! [X0] :
( zero != X0
| one != addition(one,X0)
| complement(X0,one)
| zero != multiplication(one,X0) )
| ~ spl3_6
| ~ spl3_30 ),
inference(superposition,[],[f322,f99]) ).
fof(f552,plain,
( spl3_59
| ~ spl3_7
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f285,f243,f102,f550]) ).
fof(f550,plain,
( spl3_59
<=> ! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_59])]) ).
fof(f285,plain,
( ! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0)
| ~ spl3_7
| ~ spl3_27 ),
inference(superposition,[],[f244,f103]) ).
fof(f548,plain,
( spl3_58
| ~ spl3_7
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f280,f243,f102,f546]) ).
fof(f546,plain,
( spl3_58
<=> ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_58])]) ).
fof(f280,plain,
( ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0))
| ~ spl3_7
| ~ spl3_27 ),
inference(superposition,[],[f244,f103]) ).
fof(f544,plain,
( spl3_57
| ~ spl3_6
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f252,f239,f98,f542]) ).
fof(f542,plain,
( spl3_57
<=> ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_57])]) ).
fof(f252,plain,
( ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0)
| ~ spl3_6
| ~ spl3_26 ),
inference(superposition,[],[f240,f99]) ).
fof(f540,plain,
( spl3_56
| ~ spl3_1
| ~ spl3_41 ),
inference(avatar_split_clause,[],[f455,f420,f76,f537]) ).
fof(f537,plain,
( spl3_56
<=> zero = multiplication(sK1,sK2(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_56])]) ).
fof(f420,plain,
( spl3_41
<=> ! [X0] :
( zero = multiplication(X0,sK2(X0))
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_41])]) ).
fof(f455,plain,
( zero = multiplication(sK1,sK2(sK1))
| ~ spl3_1
| ~ spl3_41 ),
inference(resolution,[],[f421,f78]) ).
fof(f421,plain,
( ! [X0] :
( ~ test(X0)
| zero = multiplication(X0,sK2(X0)) )
| ~ spl3_41 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f535,plain,
( spl3_55
| ~ spl3_6
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f247,f239,f98,f533]) ).
fof(f533,plain,
( spl3_55
<=> ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_55])]) ).
fof(f247,plain,
( ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1))
| ~ spl3_6
| ~ spl3_26 ),
inference(superposition,[],[f240,f99]) ).
fof(f531,plain,
( spl3_54
| ~ spl3_13
| ~ spl3_24 ),
inference(avatar_split_clause,[],[f214,f200,f128,f529]) ).
fof(f214,plain,
( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1))
| ~ spl3_13
| ~ spl3_24 ),
inference(superposition,[],[f201,f129]) ).
fof(f526,plain,
( spl3_53
| ~ spl3_8
| ~ spl3_24 ),
inference(avatar_split_clause,[],[f213,f200,f106,f524]) ).
fof(f524,plain,
( spl3_53
<=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_53])]) ).
fof(f106,plain,
( spl3_8
<=> ! [X0] : addition(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f213,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1)))
| ~ spl3_8
| ~ spl3_24 ),
inference(superposition,[],[f201,f107]) ).
fof(f107,plain,
( ! [X0] : addition(X0,X0) = X0
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f522,plain,
( spl3_52
| ~ spl3_13
| ~ spl3_24 ),
inference(avatar_split_clause,[],[f209,f200,f128,f520]) ).
fof(f520,plain,
( spl3_52
<=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_52])]) ).
fof(f209,plain,
( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2)
| ~ spl3_13
| ~ spl3_24 ),
inference(superposition,[],[f201,f129]) ).
fof(f517,plain,
( spl3_51
| ~ spl3_11
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f171,f168,f118,f515]) ).
fof(f515,plain,
( spl3_51
<=> ! [X0] :
( c(sK2(X0)) = X0
| ~ test(sK2(X0))
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_51])]) ).
fof(f118,plain,
( spl3_11
<=> ! [X0] :
( complement(sK2(X0),X0)
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
fof(f168,plain,
( spl3_19
<=> ! [X0,X1] :
( c(X0) = X1
| ~ complement(X0,X1)
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
fof(f171,plain,
( ! [X0] :
( c(sK2(X0)) = X0
| ~ test(sK2(X0))
| ~ test(X0) )
| ~ spl3_11
| ~ spl3_19 ),
inference(resolution,[],[f169,f119]) ).
fof(f119,plain,
( ! [X0] :
( complement(sK2(X0),X0)
| ~ test(X0) )
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f169,plain,
( ! [X0,X1] :
( ~ complement(X0,X1)
| c(X0) = X1
| ~ test(X0) )
| ~ spl3_19 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f494,plain,
( spl3_50
| ~ spl3_8
| ~ spl3_24 ),
inference(avatar_split_clause,[],[f208,f200,f106,f492]) ).
fof(f492,plain,
( spl3_50
<=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_50])]) ).
fof(f208,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1))
| ~ spl3_8
| ~ spl3_24 ),
inference(superposition,[],[f201,f107]) ).
fof(f476,plain,
( spl3_49
| ~ spl3_2
| ~ spl3_41 ),
inference(avatar_split_clause,[],[f454,f420,f81,f473]) ).
fof(f473,plain,
( spl3_49
<=> zero = multiplication(sK0,sK2(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_49])]) ).
fof(f454,plain,
( zero = multiplication(sK0,sK2(sK0))
| ~ spl3_2
| ~ spl3_41 ),
inference(resolution,[],[f421,f83]) ).
fof(f451,plain,
( spl3_48
| ~ spl3_13
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f160,f148,f128,f449]) ).
fof(f449,plain,
( spl3_48
<=> ! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_48])]) ).
fof(f160,plain,
( ! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) )
| ~ spl3_13
| ~ spl3_17 ),
inference(superposition,[],[f149,f129]) ).
fof(f447,plain,
( spl3_47
| ~ spl3_12
| ~ spl3_13
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f157,f144,f128,f122,f445]) ).
fof(f122,plain,
( spl3_12
<=> ! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f144,plain,
( spl3_16
<=> ! [X0,X1] :
( addition(X0,X1) = one
| ~ complement(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f157,plain,
( ! [X0] :
( one = addition(X0,c(X0))
| ~ test(X0) )
| ~ spl3_12
| ~ spl3_13
| ~ spl3_16 ),
inference(forward_demodulation,[],[f156,f129]) ).
fof(f156,plain,
( ! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) )
| ~ spl3_12
| ~ spl3_16 ),
inference(resolution,[],[f145,f123]) ).
fof(f123,plain,
( ! [X0] :
( complement(X0,c(X0))
| ~ test(X0) )
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f145,plain,
( ! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one )
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f443,plain,
( spl3_46
| ~ spl3_11
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f155,f144,f118,f441]) ).
fof(f441,plain,
( spl3_46
<=> ! [X0] :
( one = addition(X0,sK2(X0))
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_46])]) ).
fof(f155,plain,
( ! [X0] :
( one = addition(X0,sK2(X0))
| ~ test(X0) )
| ~ spl3_11
| ~ spl3_16 ),
inference(resolution,[],[f145,f119]) ).
fof(f439,plain,
( spl3_45
| ~ spl3_12
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f154,f140,f122,f437]) ).
fof(f437,plain,
( spl3_45
<=> ! [X0] :
( zero = multiplication(X0,c(X0))
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_45])]) ).
fof(f140,plain,
( spl3_15
<=> ! [X0,X1] :
( zero = multiplication(X1,X0)
| ~ complement(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
fof(f154,plain,
( ! [X0] :
( zero = multiplication(X0,c(X0))
| ~ test(X0) )
| ~ spl3_12
| ~ spl3_15 ),
inference(resolution,[],[f141,f123]) ).
fof(f141,plain,
( ! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) )
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f435,plain,
( spl3_44
| ~ spl3_11
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f153,f140,f118,f433]) ).
fof(f433,plain,
( spl3_44
<=> ! [X0] :
( zero = multiplication(sK2(X0),X0)
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_44])]) ).
fof(f153,plain,
( ! [X0] :
( zero = multiplication(sK2(X0),X0)
| ~ test(X0) )
| ~ spl3_11
| ~ spl3_15 ),
inference(resolution,[],[f141,f119]) ).
fof(f431,plain,
( spl3_43
| ~ spl3_2
| ~ spl3_8
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f373,f354,f106,f81,f428]) ).
fof(f428,plain,
( spl3_43
<=> c(sK0) = c(multiplication(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_43])]) ).
fof(f354,plain,
( spl3_34
<=> ! [X0] :
( c(multiplication(X0,sK0)) = addition(c(X0),c(sK0))
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).
fof(f373,plain,
( c(sK0) = c(multiplication(sK0,sK0))
| ~ spl3_2
| ~ spl3_8
| ~ spl3_34 ),
inference(forward_demodulation,[],[f371,f107]) ).
fof(f371,plain,
( c(multiplication(sK0,sK0)) = addition(c(sK0),c(sK0))
| ~ spl3_2
| ~ spl3_34 ),
inference(resolution,[],[f355,f83]) ).
fof(f355,plain,
( ! [X0] :
( ~ test(X0)
| c(multiplication(X0,sK0)) = addition(c(X0),c(sK0)) )
| ~ spl3_34 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f426,plain,
( spl3_42
| ~ spl3_12
| ~ spl3_14 ),
inference(avatar_split_clause,[],[f152,f136,f122,f424]) ).
fof(f424,plain,
( spl3_42
<=> ! [X0] :
( zero = multiplication(c(X0),X0)
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_42])]) ).
fof(f136,plain,
( spl3_14
<=> ! [X0,X1] :
( zero = multiplication(X0,X1)
| ~ complement(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f152,plain,
( ! [X0] :
( zero = multiplication(c(X0),X0)
| ~ test(X0) )
| ~ spl3_12
| ~ spl3_14 ),
inference(resolution,[],[f137,f123]) ).
fof(f137,plain,
( ! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) )
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f422,plain,
( spl3_41
| ~ spl3_11
| ~ spl3_14 ),
inference(avatar_split_clause,[],[f151,f136,f118,f420]) ).
fof(f151,plain,
( ! [X0] :
( zero = multiplication(X0,sK2(X0))
| ~ test(X0) )
| ~ spl3_11
| ~ spl3_14 ),
inference(resolution,[],[f137,f119]) ).
fof(f415,plain,
( spl3_40
| ~ spl3_3
| ~ spl3_4
| ~ spl3_5
| ~ spl3_30 ),
inference(avatar_split_clause,[],[f342,f321,f94,f90,f86,f413]) ).
fof(f413,plain,
( spl3_40
<=> ! [X0] :
( one != X0
| complement(zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_40])]) ).
fof(f86,plain,
( spl3_3
<=> ! [X0] : zero = multiplication(X0,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f90,plain,
( spl3_4
<=> ! [X0] : zero = multiplication(zero,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f94,plain,
( spl3_5
<=> ! [X0] : addition(X0,zero) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f342,plain,
( ! [X0] :
( one != X0
| complement(zero,X0) )
| ~ spl3_3
| ~ spl3_4
| ~ spl3_5
| ~ spl3_30 ),
inference(trivial_inequality_removal,[],[f341]) ).
fof(f341,plain,
( ! [X0] :
( zero != zero
| one != X0
| complement(zero,X0) )
| ~ spl3_3
| ~ spl3_4
| ~ spl3_5
| ~ spl3_30 ),
inference(forward_demodulation,[],[f340,f87]) ).
fof(f87,plain,
( ! [X0] : zero = multiplication(X0,zero)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f340,plain,
( ! [X0] :
( one != X0
| complement(zero,X0)
| zero != multiplication(X0,zero) )
| ~ spl3_4
| ~ spl3_5
| ~ spl3_30 ),
inference(forward_demodulation,[],[f333,f95]) ).
fof(f95,plain,
( ! [X0] : addition(X0,zero) = X0
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f333,plain,
( ! [X0] :
( addition(X0,zero) != one
| complement(zero,X0)
| zero != multiplication(X0,zero) )
| ~ spl3_4
| ~ spl3_30 ),
inference(trivial_inequality_removal,[],[f330]) ).
fof(f330,plain,
( ! [X0] :
( zero != zero
| addition(X0,zero) != one
| complement(zero,X0)
| zero != multiplication(X0,zero) )
| ~ spl3_4
| ~ spl3_30 ),
inference(superposition,[],[f322,f91]) ).
fof(f91,plain,
( ! [X0] : zero = multiplication(zero,X0)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f411,plain,
( spl3_39
| ~ spl3_3
| ~ spl3_4
| ~ spl3_5
| ~ spl3_13
| ~ spl3_30 ),
inference(avatar_split_clause,[],[f337,f321,f128,f94,f90,f86,f409]) ).
fof(f409,plain,
( spl3_39
<=> ! [X0] :
( one != X0
| complement(X0,zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_39])]) ).
fof(f337,plain,
( ! [X0] :
( one != X0
| complement(X0,zero) )
| ~ spl3_3
| ~ spl3_4
| ~ spl3_5
| ~ spl3_13
| ~ spl3_30 ),
inference(trivial_inequality_removal,[],[f336]) ).
fof(f336,plain,
( ! [X0] :
( zero != zero
| one != X0
| complement(X0,zero) )
| ~ spl3_3
| ~ spl3_4
| ~ spl3_5
| ~ spl3_13
| ~ spl3_30 ),
inference(forward_demodulation,[],[f335,f91]) ).
fof(f335,plain,
( ! [X0] :
( one != X0
| complement(X0,zero)
| zero != multiplication(zero,X0) )
| ~ spl3_3
| ~ spl3_5
| ~ spl3_13
| ~ spl3_30 ),
inference(forward_demodulation,[],[f334,f131]) ).
fof(f131,plain,
( ! [X0] : addition(zero,X0) = X0
| ~ spl3_5
| ~ spl3_13 ),
inference(superposition,[],[f129,f95]) ).
fof(f334,plain,
( ! [X0] :
( one != addition(zero,X0)
| complement(X0,zero)
| zero != multiplication(zero,X0) )
| ~ spl3_3
| ~ spl3_30 ),
inference(trivial_inequality_removal,[],[f328]) ).
fof(f328,plain,
( ! [X0] :
( zero != zero
| one != addition(zero,X0)
| complement(X0,zero)
| zero != multiplication(zero,X0) )
| ~ spl3_3
| ~ spl3_30 ),
inference(superposition,[],[f322,f87]) ).
fof(f407,plain,
( spl3_38
| ~ spl3_5
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f158,f148,f94,f405]) ).
fof(f405,plain,
( spl3_38
<=> ! [X0] :
( zero != X0
| leq(X0,zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_38])]) ).
fof(f158,plain,
( ! [X0] :
( zero != X0
| leq(X0,zero) )
| ~ spl3_5
| ~ spl3_17 ),
inference(superposition,[],[f149,f95]) ).
fof(f386,plain,
( spl3_37
| ~ spl3_1
| ~ spl3_8
| ~ spl3_33 ),
inference(avatar_split_clause,[],[f369,f350,f106,f76,f383]) ).
fof(f383,plain,
( spl3_37
<=> c(sK1) = c(multiplication(sK1,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).
fof(f350,plain,
( spl3_33
<=> ! [X0] :
( c(multiplication(X0,sK1)) = addition(c(X0),c(sK1))
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).
fof(f369,plain,
( c(sK1) = c(multiplication(sK1,sK1))
| ~ spl3_1
| ~ spl3_8
| ~ spl3_33 ),
inference(forward_demodulation,[],[f366,f107]) ).
fof(f366,plain,
( c(multiplication(sK1,sK1)) = addition(c(sK1),c(sK1))
| ~ spl3_1
| ~ spl3_33 ),
inference(resolution,[],[f351,f78]) ).
fof(f351,plain,
( ! [X0] :
( ~ test(X0)
| c(multiplication(X0,sK1)) = addition(c(X0),c(sK1)) )
| ~ spl3_33 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f381,plain,
( spl3_36
| ~ spl3_5
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f131,f128,f94,f379]) ).
fof(f379,plain,
( spl3_36
<=> ! [X0] : addition(zero,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).
fof(f377,plain,
( spl3_35
| ~ spl3_9
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f126,f122,f110,f375]) ).
fof(f375,plain,
( spl3_35
<=> ! [X0] :
( ~ test(X0)
| test(c(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_35])]) ).
fof(f110,plain,
( spl3_9
<=> ! [X0,X1] :
( test(X0)
| ~ complement(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f126,plain,
( ! [X0] :
( ~ test(X0)
| test(c(X0)) )
| ~ spl3_9
| ~ spl3_12 ),
inference(resolution,[],[f123,f111]) ).
fof(f111,plain,
( ! [X0,X1] :
( ~ complement(X1,X0)
| test(X0) )
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f356,plain,
( spl3_34
| ~ spl3_2
| ~ spl3_29 ),
inference(avatar_split_clause,[],[f318,f311,f81,f354]) ).
fof(f318,plain,
( ! [X0] :
( c(multiplication(X0,sK0)) = addition(c(X0),c(sK0))
| ~ test(X0) )
| ~ spl3_2
| ~ spl3_29 ),
inference(resolution,[],[f312,f83]) ).
fof(f352,plain,
( spl3_33
| ~ spl3_1
| ~ spl3_29 ),
inference(avatar_split_clause,[],[f317,f311,f76,f350]) ).
fof(f317,plain,
( ! [X0] :
( c(multiplication(X0,sK1)) = addition(c(X0),c(sK1))
| ~ test(X0) )
| ~ spl3_1
| ~ spl3_29 ),
inference(resolution,[],[f312,f78]) ).
fof(f348,plain,
( spl3_32
| ~ spl3_2
| ~ spl3_28 ),
inference(avatar_split_clause,[],[f315,f307,f81,f346]) ).
fof(f346,plain,
( spl3_32
<=> ! [X0] :
( multiplication(c(X0),c(sK0)) = c(addition(X0,sK0))
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).
fof(f315,plain,
( ! [X0] :
( multiplication(c(X0),c(sK0)) = c(addition(X0,sK0))
| ~ test(X0) )
| ~ spl3_2
| ~ spl3_28 ),
inference(resolution,[],[f308,f83]) ).
fof(f327,plain,
( spl3_31
| ~ spl3_1
| ~ spl3_28 ),
inference(avatar_split_clause,[],[f314,f307,f76,f325]) ).
fof(f325,plain,
( spl3_31
<=> ! [X0] :
( multiplication(c(X0),c(sK1)) = c(addition(X0,sK1))
| ~ test(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).
fof(f314,plain,
( ! [X0] :
( multiplication(c(X0),c(sK1)) = c(addition(X0,sK1))
| ~ test(X0) )
| ~ spl3_1
| ~ spl3_28 ),
inference(resolution,[],[f308,f78]) ).
fof(f323,plain,
spl3_30,
inference(avatar_split_clause,[],[f68,f321]) ).
fof(f68,plain,
! [X0,X1] :
( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) )
& ( ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) )
& ( ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X3,X4] :
( complement(X4,X3)
<=> ( one = addition(X3,X4)
& zero = multiplication(X4,X3)
& zero = multiplication(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
fof(f313,plain,
spl3_29,
inference(avatar_split_clause,[],[f64,f311]) ).
fof(f64,plain,
! [X0,X1] :
( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X1)
| ~ test(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X3,X4] :
( ( test(X4)
& test(X3) )
=> c(multiplication(X3,X4)) = addition(c(X3),c(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan2) ).
fof(f309,plain,
spl3_28,
inference(avatar_split_clause,[],[f63,f307]) ).
fof(f63,plain,
! [X0,X1] :
( multiplication(c(X0),c(X1)) = c(addition(X0,X1))
| ~ test(X1)
| ~ test(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( multiplication(c(X0),c(X1)) = c(addition(X0,X1))
| ~ test(X1)
| ~ test(X0) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( multiplication(c(X0),c(X1)) = c(addition(X0,X1))
| ~ test(X1)
| ~ test(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> multiplication(c(X0),c(X1)) = c(addition(X0,X1)) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X3,X4] :
( ( test(X4)
& test(X3) )
=> c(addition(X3,X4)) = multiplication(c(X3),c(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan1) ).
fof(f245,plain,
spl3_27,
inference(avatar_split_clause,[],[f73,f243]) ).
fof(f73,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/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f241,plain,
spl3_26,
inference(avatar_split_clause,[],[f72,f239]) ).
fof(f72,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/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f206,plain,
spl3_25,
inference(avatar_split_clause,[],[f71,f204]) ).
fof(f71,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/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f202,plain,
spl3_24,
inference(avatar_split_clause,[],[f70,f200]) ).
fof(f70,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f28]) ).
fof(f28,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/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f198,plain,
( ~ spl3_23
| ~ spl3_13
| spl3_20 ),
inference(avatar_split_clause,[],[f188,f175,f128,f195]) ).
fof(f175,plain,
( spl3_20
<=> leq(one,addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
fof(f188,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1))))))
| ~ spl3_13
| spl3_20 ),
inference(forward_demodulation,[],[f187,f72]) ).
fof(f187,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))))))
| ~ spl3_13
| spl3_20 ),
inference(forward_demodulation,[],[f186,f129]) ).
fof(f186,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1))))
| ~ spl3_13
| spl3_20 ),
inference(forward_demodulation,[],[f177,f129]) ).
fof(f177,plain,
( ~ leq(one,addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))))
| spl3_20 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f193,plain,
( ~ spl3_22
| ~ spl3_13
| spl3_21 ),
inference(avatar_split_clause,[],[f185,f179,f128,f190]) ).
fof(f179,plain,
( spl3_21
<=> leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
fof(f185,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1))))),one)
| ~ spl3_13
| spl3_21 ),
inference(forward_demodulation,[],[f184,f72]) ).
fof(f184,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))))),one)
| ~ spl3_13
| spl3_21 ),
inference(forward_demodulation,[],[f183,f129]) ).
fof(f183,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1))),one)
| ~ spl3_13
| spl3_21 ),
inference(forward_demodulation,[],[f181,f129]) ).
fof(f181,plain,
( ~ leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
| spl3_21 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,plain,
( ~ spl3_20
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f50,f179,f175]) ).
fof(f50,plain,
( ~ leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( ( ~ leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) )
& test(sK0)
& test(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f31,f39]) ).
fof(f39,plain,
( ? [X0,X1] :
( ( ~ leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) )
=> ( ( ~ leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) )
& test(sK0)
& test(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
? [X0,X1] :
( ( ~ leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
? [X0,X1] :
( ( ~ leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3,X4] :
( ( test(X3)
& test(X4) )
=> ( leq(addition(addition(addition(multiplication(X3,X4),multiplication(X3,c(X4))),multiplication(c(X3),X4)),multiplication(c(X3),c(X4))),one)
& leq(one,addition(addition(addition(multiplication(X3,X4),multiplication(X3,c(X4))),multiplication(c(X3),X4)),multiplication(c(X3),c(X4)))) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3,X4] :
( ( test(X3)
& test(X4) )
=> ( leq(addition(addition(addition(multiplication(X3,X4),multiplication(X3,c(X4))),multiplication(c(X3),X4)),multiplication(c(X3),c(X4))),one)
& leq(one,addition(addition(addition(multiplication(X3,X4),multiplication(X3,c(X4))),multiplication(c(X3),X4)),multiplication(c(X3),c(X4)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f170,plain,
spl3_19,
inference(avatar_split_clause,[],[f62,f168]) ).
fof(f62,plain,
! [X0,X1] :
( c(X0) = X1
| ~ complement(X0,X1)
| ~ test(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3,X4] :
( test(X3)
=> ( c(X3) = X4
<=> complement(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
fof(f166,plain,
( spl3_18
| ~ spl3_8
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f162,f148,f106,f164]) ).
fof(f162,plain,
( ! [X0] : leq(X0,X0)
| ~ spl3_8
| ~ spl3_17 ),
inference(trivial_inequality_removal,[],[f159]) ).
fof(f159,plain,
( ! [X0] :
( X0 != X0
| leq(X0,X0) )
| ~ spl3_8
| ~ spl3_17 ),
inference(superposition,[],[f149,f107]) ).
fof(f150,plain,
spl3_17,
inference(avatar_split_clause,[],[f69,f148]) ).
fof(f69,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f146,plain,
spl3_16,
inference(avatar_split_clause,[],[f67,f144]) ).
fof(f67,plain,
! [X0,X1] :
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f142,plain,
spl3_15,
inference(avatar_split_clause,[],[f66,f140]) ).
fof(f66,plain,
! [X0,X1] :
( zero = multiplication(X1,X0)
| ~ complement(X1,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f138,plain,
spl3_14,
inference(avatar_split_clause,[],[f65,f136]) ).
fof(f65,plain,
! [X0,X1] :
( zero = multiplication(X0,X1)
| ~ complement(X1,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f130,plain,
spl3_13,
inference(avatar_split_clause,[],[f60,f128]) ).
fof(f60,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/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f124,plain,
spl3_12,
inference(avatar_split_clause,[],[f74,f122]) ).
fof(f74,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f120,plain,
spl3_11,
inference(avatar_split_clause,[],[f58,f118]) ).
fof(f58,plain,
! [X0] :
( complement(sK2(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK2(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f42,f43]) ).
fof(f43,plain,
! [X0] :
( ? [X2] : complement(X2,X0)
=> complement(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(rectify,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] :
( test(X3)
<=> ? [X4] : complement(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
fof(f116,plain,
spl3_10,
inference(avatar_split_clause,[],[f57,f114]) ).
fof(f57,plain,
! [X0] :
( zero = c(X0)
| test(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( zero = c(X0)
| test(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] :
( ~ test(X0)
=> zero = c(X0) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X3] :
( ~ test(X3)
=> zero = c(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
fof(f112,plain,
spl3_9,
inference(avatar_split_clause,[],[f59,f110]) ).
fof(f59,plain,
! [X0,X1] :
( test(X0)
| ~ complement(X1,X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f108,plain,
spl3_8,
inference(avatar_split_clause,[],[f56,f106]) ).
fof(f56,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f104,plain,
spl3_7,
inference(avatar_split_clause,[],[f55,f102]) ).
fof(f55,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f100,plain,
spl3_6,
inference(avatar_split_clause,[],[f54,f98]) ).
fof(f54,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f96,plain,
spl3_5,
inference(avatar_split_clause,[],[f53,f94]) ).
fof(f53,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f92,plain,
spl3_4,
inference(avatar_split_clause,[],[f52,f90]) ).
fof(f52,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f88,plain,
spl3_3,
inference(avatar_split_clause,[],[f51,f86]) ).
fof(f51,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(X0,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
fof(f84,plain,
spl3_2,
inference(avatar_split_clause,[],[f49,f81]) ).
fof(f49,plain,
test(sK0),
inference(cnf_transformation,[],[f40]) ).
fof(f79,plain,
spl3_1,
inference(avatar_split_clause,[],[f48,f76]) ).
fof(f48,plain,
test(sK1),
inference(cnf_transformation,[],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : KLE009+4 : 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 : n013.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 : Fri May 3 21:23:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (2280)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (2285)WARNING: value z3 for option sas not known
% 0.14/0.38 % (2286)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (2284)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 % (2287)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 % (2285)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 % (2283)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (2288)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 % (2289)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 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [4]
% 0.14/0.39 TRYING [3]
% 0.14/0.40 TRYING [3]
% 0.21/0.41 TRYING [4]
% 0.21/0.42 % (2287)First to succeed.
% 0.21/0.42 % (2288)Also succeeded, but the first one will report.
% 0.21/0.43 % (2287)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2280"
% 0.21/0.43 TRYING [5]
% 0.21/0.43 % (2287)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Theorem for theBenchmark
% 0.21/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.43 % (2287)------------------------------
% 0.21/0.43 % (2287)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.43 % (2287)Termination reason: Refutation
% 0.21/0.43
% 0.21/0.43 % (2287)Memory used [KB]: 1466
% 0.21/0.43 % (2287)Time elapsed: 0.052 s
% 0.21/0.43 % (2287)Instructions burned: 85 (million)
% 0.21/0.43 % (2280)Success in time 0.067 s
%------------------------------------------------------------------------------