TSTP Solution File: KLE089+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE089+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 : 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 : Tue Apr 30 13:11:54 EDT 2024
% Result : Theorem 0.21s 0.40s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 64
% Syntax : Number of formulae : 198 ( 68 unt; 0 def)
% Number of atoms : 415 ( 160 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 391 ( 174 ~; 165 |; 4 &)
% ( 44 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 46 ( 44 usr; 45 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 227 ( 223 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f708,plain,
$false,
inference(avatar_sat_refutation,[],[f63,f68,f72,f76,f80,f84,f88,f92,f96,f100,f108,f120,f125,f129,f141,f145,f188,f192,f271,f275,f314,f326,f331,f339,f347,f356,f360,f364,f368,f404,f432,f461,f465,f469,f473,f477,f563,f681,f685,f690,f694,f698,f702,f706,f707]) ).
fof(f707,plain,
( spl2_1
| ~ spl2_10
| ~ spl2_13
| ~ spl2_35 ),
inference(avatar_split_clause,[],[f630,f471,f122,f98,f60]) ).
fof(f60,plain,
( spl2_1
<=> zero = multiplication(antidomain(antidomain(sK0)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f98,plain,
( spl2_10
<=> ! [X0] : zero = multiplication(antidomain(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
fof(f122,plain,
( spl2_13
<=> antidomain(sK1) = addition(antidomain(sK1),antidomain(antidomain(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
fof(f471,plain,
( spl2_35
<=> ! [X0,X1] : multiplication(X1,X0) = multiplication(addition(antidomain(X0),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_35])]) ).
fof(f630,plain,
( zero = multiplication(antidomain(antidomain(sK0)),sK1)
| ~ spl2_10
| ~ spl2_13
| ~ spl2_35 ),
inference(forward_demodulation,[],[f608,f99]) ).
fof(f99,plain,
( ! [X0] : zero = multiplication(antidomain(X0),X0)
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f608,plain,
( multiplication(antidomain(antidomain(sK0)),sK1) = multiplication(antidomain(sK1),sK1)
| ~ spl2_13
| ~ spl2_35 ),
inference(superposition,[],[f472,f124]) ).
fof(f124,plain,
( antidomain(sK1) = addition(antidomain(sK1),antidomain(antidomain(sK0)))
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f472,plain,
( ! [X0,X1] : multiplication(X1,X0) = multiplication(addition(antidomain(X0),X1),X0)
| ~ spl2_35 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f706,plain,
( spl2_44
| ~ spl2_5
| ~ spl2_10
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f229,f186,f98,f78,f704]) ).
fof(f704,plain,
( spl2_44
<=> ! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_44])]) ).
fof(f78,plain,
( spl2_5
<=> ! [X0] : addition(X0,zero) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
fof(f186,plain,
( spl2_17
<=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
fof(f229,plain,
( ! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X1,X0))
| ~ spl2_5
| ~ spl2_10
| ~ spl2_17 ),
inference(forward_demodulation,[],[f206,f79]) ).
fof(f79,plain,
( ! [X0] : addition(X0,zero) = X0
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f206,plain,
( ! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero)
| ~ spl2_10
| ~ spl2_17 ),
inference(superposition,[],[f187,f99]) ).
fof(f187,plain,
( ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2))
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f702,plain,
( spl2_43
| ~ spl2_5
| ~ spl2_10
| ~ spl2_11
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f221,f186,f106,f98,f78,f700]) ).
fof(f700,plain,
( spl2_43
<=> ! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_43])]) ).
fof(f106,plain,
( spl2_11
<=> ! [X0,X1] : addition(X0,X1) = addition(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
fof(f221,plain,
( ! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1)
| ~ spl2_5
| ~ spl2_10
| ~ spl2_11
| ~ spl2_17 ),
inference(forward_demodulation,[],[f199,f110]) ).
fof(f110,plain,
( ! [X0] : addition(zero,X0) = X0
| ~ spl2_5
| ~ spl2_11 ),
inference(superposition,[],[f107,f79]) ).
fof(f107,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X1,X0)
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f199,plain,
( ! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1))
| ~ spl2_10
| ~ spl2_17 ),
inference(superposition,[],[f187,f99]) ).
fof(f698,plain,
( spl2_42
| ~ spl2_6
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f201,f186,f82,f696]) ).
fof(f696,plain,
( spl2_42
<=> ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_42])]) ).
fof(f82,plain,
( spl2_6
<=> ! [X0] : multiplication(X0,one) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
fof(f201,plain,
( ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0)
| ~ spl2_6
| ~ spl2_17 ),
inference(superposition,[],[f187,f83]) ).
fof(f83,plain,
( ! [X0] : multiplication(X0,one) = X0
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f694,plain,
( spl2_41
| ~ spl2_6
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f194,f186,f82,f692]) ).
fof(f692,plain,
( spl2_41
<=> ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_41])]) ).
fof(f194,plain,
( ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1))
| ~ spl2_6
| ~ spl2_17 ),
inference(superposition,[],[f187,f83]) ).
fof(f690,plain,
( spl2_40
| ~ spl2_11
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f156,f139,f106,f688]) ).
fof(f688,plain,
( spl2_40
<=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_40])]) ).
fof(f139,plain,
( spl2_15
<=> ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
fof(f156,plain,
( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1))
| ~ spl2_11
| ~ spl2_15 ),
inference(superposition,[],[f140,f107]) ).
fof(f140,plain,
( ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0)
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f685,plain,
( spl2_39
| ~ spl2_8
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f155,f139,f90,f683]) ).
fof(f683,plain,
( spl2_39
<=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_39])]) ).
fof(f90,plain,
( spl2_8
<=> ! [X0] : addition(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
fof(f155,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1)))
| ~ spl2_8
| ~ spl2_15 ),
inference(superposition,[],[f140,f91]) ).
fof(f91,plain,
( ! [X0] : addition(X0,X0) = X0
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f681,plain,
( spl2_38
| ~ spl2_11
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f148,f139,f106,f679]) ).
fof(f679,plain,
( spl2_38
<=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_38])]) ).
fof(f148,plain,
( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2)
| ~ spl2_11
| ~ spl2_15 ),
inference(superposition,[],[f140,f107]) ).
fof(f563,plain,
( spl2_37
| ~ spl2_11
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f318,f312,f106,f561]) ).
fof(f561,plain,
( spl2_37
<=> ! [X0] : addition(X0,antidomain(sK1)) = addition(antidomain(antidomain(sK0)),addition(X0,antidomain(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_37])]) ).
fof(f312,plain,
( spl2_21
<=> ! [X0] : addition(antidomain(sK1),X0) = addition(antidomain(antidomain(sK0)),addition(antidomain(sK1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).
fof(f318,plain,
( ! [X0] : addition(X0,antidomain(sK1)) = addition(antidomain(antidomain(sK0)),addition(X0,antidomain(sK1)))
| ~ spl2_11
| ~ spl2_21 ),
inference(superposition,[],[f313,f107]) ).
fof(f313,plain,
( ! [X0] : addition(antidomain(sK1),X0) = addition(antidomain(antidomain(sK0)),addition(antidomain(sK1),X0))
| ~ spl2_21 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f477,plain,
( spl2_36
| ~ spl2_5
| ~ spl2_10
| ~ spl2_18 ),
inference(avatar_split_clause,[],[f265,f190,f98,f78,f475]) ).
fof(f475,plain,
( spl2_36
<=> ! [X0,X1] : multiplication(X1,X0) = multiplication(addition(X1,antidomain(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_36])]) ).
fof(f190,plain,
( spl2_18
<=> ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
fof(f265,plain,
( ! [X0,X1] : multiplication(X1,X0) = multiplication(addition(X1,antidomain(X0)),X0)
| ~ spl2_5
| ~ spl2_10
| ~ spl2_18 ),
inference(forward_demodulation,[],[f244,f79]) ).
fof(f244,plain,
( ! [X0,X1] : addition(multiplication(X1,X0),zero) = multiplication(addition(X1,antidomain(X0)),X0)
| ~ spl2_10
| ~ spl2_18 ),
inference(superposition,[],[f191,f99]) ).
fof(f191,plain,
( ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2))
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f473,plain,
( spl2_35
| ~ spl2_5
| ~ spl2_10
| ~ spl2_11
| ~ spl2_18 ),
inference(avatar_split_clause,[],[f259,f190,f106,f98,f78,f471]) ).
fof(f259,plain,
( ! [X0,X1] : multiplication(X1,X0) = multiplication(addition(antidomain(X0),X1),X0)
| ~ spl2_5
| ~ spl2_10
| ~ spl2_11
| ~ spl2_18 ),
inference(forward_demodulation,[],[f237,f110]) ).
fof(f237,plain,
( ! [X0,X1] : addition(zero,multiplication(X1,X0)) = multiplication(addition(antidomain(X0),X1),X0)
| ~ spl2_10
| ~ spl2_18 ),
inference(superposition,[],[f191,f99]) ).
fof(f469,plain,
( spl2_34
| ~ spl2_5
| ~ spl2_9
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f223,f186,f94,f78,f467]) ).
fof(f467,plain,
( spl2_34
<=> ! [X0,X1] : multiplication(X0,X1) = multiplication(X0,addition(X1,coantidomain(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_34])]) ).
fof(f94,plain,
( spl2_9
<=> ! [X0] : zero = multiplication(X0,coantidomain(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
fof(f223,plain,
( ! [X0,X1] : multiplication(X0,X1) = multiplication(X0,addition(X1,coantidomain(X0)))
| ~ spl2_5
| ~ spl2_9
| ~ spl2_17 ),
inference(forward_demodulation,[],[f202,f79]) ).
fof(f202,plain,
( ! [X0,X1] : addition(multiplication(X0,X1),zero) = multiplication(X0,addition(X1,coantidomain(X0)))
| ~ spl2_9
| ~ spl2_17 ),
inference(superposition,[],[f187,f95]) ).
fof(f95,plain,
( ! [X0] : zero = multiplication(X0,coantidomain(X0))
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f465,plain,
( spl2_33
| ~ spl2_5
| ~ spl2_9
| ~ spl2_11
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f215,f186,f106,f94,f78,f463]) ).
fof(f463,plain,
( spl2_33
<=> ! [X0,X1] : multiplication(X0,X1) = multiplication(X0,addition(coantidomain(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).
fof(f215,plain,
( ! [X0,X1] : multiplication(X0,X1) = multiplication(X0,addition(coantidomain(X0),X1))
| ~ spl2_5
| ~ spl2_9
| ~ spl2_11
| ~ spl2_17 ),
inference(forward_demodulation,[],[f195,f110]) ).
fof(f195,plain,
( ! [X0,X1] : addition(zero,multiplication(X0,X1)) = multiplication(X0,addition(coantidomain(X0),X1))
| ~ spl2_9
| ~ spl2_17 ),
inference(superposition,[],[f187,f95]) ).
fof(f461,plain,
( spl2_32
| ~ spl2_9
| ~ spl2_16 ),
inference(avatar_split_clause,[],[f173,f143,f94,f459]) ).
fof(f459,plain,
( spl2_32
<=> ! [X0,X1] : zero = multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).
fof(f143,plain,
( spl2_16
<=> ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
fof(f173,plain,
( ! [X0,X1] : zero = multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1))))
| ~ spl2_9
| ~ spl2_16 ),
inference(superposition,[],[f144,f95]) ).
fof(f144,plain,
( ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2)
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f432,plain,
( spl2_31
| ~ spl2_8
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f147,f139,f90,f430]) ).
fof(f430,plain,
( spl2_31
<=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).
fof(f147,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1))
| ~ spl2_8
| ~ spl2_15 ),
inference(superposition,[],[f140,f91]) ).
fof(f404,plain,
( spl2_30
| ~ spl2_21
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f372,f358,f312,f401]) ).
fof(f401,plain,
( spl2_30
<=> one = addition(antidomain(antidomain(sK0)),one) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).
fof(f358,plain,
( spl2_27
<=> ! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).
fof(f372,plain,
( one = addition(antidomain(antidomain(sK0)),one)
| ~ spl2_21
| ~ spl2_27 ),
inference(superposition,[],[f313,f359]) ).
fof(f359,plain,
( ! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0)))
| ~ spl2_27 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f368,plain,
( spl2_29
| ~ spl2_4
| ~ spl2_10
| ~ spl2_16 ),
inference(avatar_split_clause,[],[f182,f143,f98,f74,f366]) ).
fof(f366,plain,
( spl2_29
<=> ! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).
fof(f74,plain,
( spl2_4
<=> ! [X0] : zero = multiplication(zero,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f182,plain,
( ! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(X0,X1))
| ~ spl2_4
| ~ spl2_10
| ~ spl2_16 ),
inference(forward_demodulation,[],[f170,f75]) ).
fof(f75,plain,
( ! [X0] : zero = multiplication(zero,X0)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f170,plain,
( ! [X0,X1] : multiplication(zero,X1) = multiplication(antidomain(X0),multiplication(X0,X1))
| ~ spl2_10
| ~ spl2_16 ),
inference(superposition,[],[f144,f99]) ).
fof(f364,plain,
( spl2_28
| ~ spl2_4
| ~ spl2_9
| ~ spl2_16 ),
inference(avatar_split_clause,[],[f178,f143,f94,f74,f362]) ).
fof(f362,plain,
( spl2_28
<=> ! [X0,X1] : zero = multiplication(X0,multiplication(coantidomain(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).
fof(f178,plain,
( ! [X0,X1] : zero = multiplication(X0,multiplication(coantidomain(X0),X1))
| ~ spl2_4
| ~ spl2_9
| ~ spl2_16 ),
inference(forward_demodulation,[],[f166,f75]) ).
fof(f166,plain,
( ! [X0,X1] : multiplication(zero,X1) = multiplication(X0,multiplication(coantidomain(X0),X1))
| ~ spl2_9
| ~ spl2_16 ),
inference(superposition,[],[f144,f95]) ).
fof(f360,plain,
( spl2_27
| ~ spl2_11
| ~ spl2_14 ),
inference(avatar_split_clause,[],[f134,f127,f106,f358]) ).
fof(f127,plain,
( spl2_14
<=> ! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
fof(f134,plain,
( ! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0)))
| ~ spl2_11
| ~ spl2_14 ),
inference(superposition,[],[f128,f107]) ).
fof(f128,plain,
( ! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0))
| ~ spl2_14 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f356,plain,
( spl2_26
| ~ spl2_11
| ~ spl2_12 ),
inference(avatar_split_clause,[],[f130,f118,f106,f354]) ).
fof(f354,plain,
( spl2_26
<=> ! [X0] : one = addition(coantidomain(X0),coantidomain(coantidomain(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).
fof(f118,plain,
( spl2_12
<=> ! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
fof(f130,plain,
( ! [X0] : one = addition(coantidomain(X0),coantidomain(coantidomain(X0)))
| ~ spl2_11
| ~ spl2_12 ),
inference(superposition,[],[f119,f107]) ).
fof(f119,plain,
( ! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0))
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f347,plain,
( spl2_25
| ~ spl2_5
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f110,f106,f78,f345]) ).
fof(f345,plain,
( spl2_25
<=> ! [X0] : addition(zero,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).
fof(f339,plain,
( spl2_24
| ~ spl2_13
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f230,f139,f122,f337]) ).
fof(f337,plain,
( spl2_24
<=> ! [X0] : addition(antidomain(sK1),X0) = addition(antidomain(sK1),addition(antidomain(antidomain(sK0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).
fof(f230,plain,
( ! [X0] : addition(antidomain(sK1),X0) = addition(antidomain(sK1),addition(antidomain(antidomain(sK0)),X0))
| ~ spl2_13
| ~ spl2_15 ),
inference(superposition,[],[f140,f124]) ).
fof(f331,plain,
( spl2_23
| ~ spl2_6
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f103,f98,f82,f328]) ).
fof(f328,plain,
( spl2_23
<=> zero = antidomain(one) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).
fof(f103,plain,
( zero = antidomain(one)
| ~ spl2_6
| ~ spl2_10 ),
inference(superposition,[],[f99,f83]) ).
fof(f326,plain,
( spl2_22
| ~ spl2_7
| ~ spl2_9 ),
inference(avatar_split_clause,[],[f101,f94,f86,f323]) ).
fof(f323,plain,
( spl2_22
<=> zero = coantidomain(one) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).
fof(f86,plain,
( spl2_7
<=> ! [X0] : multiplication(one,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
fof(f101,plain,
( zero = coantidomain(one)
| ~ spl2_7
| ~ spl2_9 ),
inference(superposition,[],[f95,f87]) ).
fof(f87,plain,
( ! [X0] : multiplication(one,X0) = X0
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f314,plain,
( spl2_21
| ~ spl2_2
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f151,f139,f65,f312]) ).
fof(f65,plain,
( spl2_2
<=> antidomain(sK1) = addition(antidomain(antidomain(sK0)),antidomain(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f151,plain,
( ! [X0] : addition(antidomain(sK1),X0) = addition(antidomain(antidomain(sK0)),addition(antidomain(sK1),X0))
| ~ spl2_2
| ~ spl2_15 ),
inference(superposition,[],[f140,f67]) ).
fof(f67,plain,
( antidomain(sK1) = addition(antidomain(antidomain(sK0)),antidomain(sK1))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f275,plain,
spl2_20,
inference(avatar_split_clause,[],[f52,f273]) ).
fof(f273,plain,
( spl2_20
<=> ! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
fof(f52,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X3,X4] : antidomain(multiplication(X3,antidomain(antidomain(X4)))) = addition(antidomain(multiplication(X3,X4)),antidomain(multiplication(X3,antidomain(antidomain(X4))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f271,plain,
spl2_19,
inference(avatar_split_clause,[],[f51,f269]) ).
fof(f269,plain,
( spl2_19
<=> ! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
fof(f51,plain,
! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X3,X4] : coantidomain(multiplication(coantidomain(coantidomain(X3)),X4)) = addition(coantidomain(multiplication(X3,X4)),coantidomain(multiplication(coantidomain(coantidomain(X3)),X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain2) ).
fof(f192,plain,
spl2_18,
inference(avatar_split_clause,[],[f56,f190]) ).
fof(f56,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(f188,plain,
spl2_17,
inference(avatar_split_clause,[],[f55,f186]) ).
fof(f55,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(f145,plain,
spl2_16,
inference(avatar_split_clause,[],[f54,f143]) ).
fof(f54,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(f141,plain,
spl2_15,
inference(avatar_split_clause,[],[f53,f139]) ).
fof(f53,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f32]) ).
fof(f32,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(f129,plain,
spl2_14,
inference(avatar_split_clause,[],[f49,f127]) ).
fof(f49,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3] : one = addition(antidomain(antidomain(X3)),antidomain(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f125,plain,
( spl2_13
| ~ spl2_2
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f109,f106,f65,f122]) ).
fof(f109,plain,
( antidomain(sK1) = addition(antidomain(sK1),antidomain(antidomain(sK0)))
| ~ spl2_2
| ~ spl2_11 ),
inference(superposition,[],[f107,f67]) ).
fof(f120,plain,
spl2_12,
inference(avatar_split_clause,[],[f48,f118]) ).
fof(f48,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X3] : one = addition(coantidomain(coantidomain(X3)),coantidomain(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain3) ).
fof(f108,plain,
spl2_11,
inference(avatar_split_clause,[],[f50,f106]) ).
fof(f50,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(f100,plain,
spl2_10,
inference(avatar_split_clause,[],[f45,f98]) ).
fof(f45,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] : zero = multiplication(antidomain(X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f96,plain,
spl2_9,
inference(avatar_split_clause,[],[f44,f94]) ).
fof(f44,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X3] : zero = multiplication(X3,coantidomain(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain1) ).
fof(f92,plain,
spl2_8,
inference(avatar_split_clause,[],[f43,f90]) ).
fof(f43,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(f88,plain,
spl2_7,
inference(avatar_split_clause,[],[f42,f86]) ).
fof(f42,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(f84,plain,
spl2_6,
inference(avatar_split_clause,[],[f41,f82]) ).
fof(f41,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(f80,plain,
spl2_5,
inference(avatar_split_clause,[],[f40,f78]) ).
fof(f40,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(f76,plain,
spl2_4,
inference(avatar_split_clause,[],[f39,f74]) ).
fof(f39,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(f72,plain,
spl2_3,
inference(avatar_split_clause,[],[f38,f70]) ).
fof(f70,plain,
( spl2_3
<=> ! [X0] : zero = multiplication(X0,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f38,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(f68,plain,
spl2_2,
inference(avatar_split_clause,[],[f58,f65]) ).
fof(f58,plain,
antidomain(sK1) = addition(antidomain(antidomain(sK0)),antidomain(sK1)),
inference(definition_unfolding,[],[f36,f47]) ).
fof(f47,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X3] : antidomain(antidomain(X3)) = domain(X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f36,plain,
antidomain(sK1) = addition(domain(sK0),antidomain(sK1)),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
( zero != multiplication(domain(sK0),sK1)
& antidomain(sK1) = addition(domain(sK0),antidomain(sK1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f33,f34]) ).
fof(f34,plain,
( ? [X0,X1] :
( zero != multiplication(domain(X0),X1)
& antidomain(X1) = addition(domain(X0),antidomain(X1)) )
=> ( zero != multiplication(domain(sK0),sK1)
& antidomain(sK1) = addition(domain(sK0),antidomain(sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
? [X0,X1] :
( zero != multiplication(domain(X0),X1)
& antidomain(X1) = addition(domain(X0),antidomain(X1)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
~ ! [X0,X1] :
( antidomain(X1) = addition(domain(X0),antidomain(X1))
=> zero = multiplication(domain(X0),X1) ),
inference(rectify,[],[f22]) ).
fof(f22,negated_conjecture,
~ ! [X3,X4] :
( antidomain(X4) = addition(domain(X3),antidomain(X4))
=> zero = multiplication(domain(X3),X4) ),
inference(negated_conjecture,[],[f21]) ).
fof(f21,conjecture,
! [X3,X4] :
( antidomain(X4) = addition(domain(X3),antidomain(X4))
=> zero = multiplication(domain(X3),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f63,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f57,f60]) ).
fof(f57,plain,
zero != multiplication(antidomain(antidomain(sK0)),sK1),
inference(definition_unfolding,[],[f37,f47]) ).
fof(f37,plain,
zero != multiplication(domain(sK0),sK1),
inference(cnf_transformation,[],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE089+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 04:56:34 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (21866)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (21869)WARNING: value z3 for option sas not known
% 0.14/0.38 % (21867)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (21870)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (21868)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 % (21872)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 % (21871)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 % (21869)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 % (21873)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]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.21/0.40 TRYING [4]
% 0.21/0.40 % (21871)First to succeed.
% 0.21/0.40 % (21871)Refutation found. Thanks to Tanya!
% 0.21/0.40 % SZS status Theorem for theBenchmark
% 0.21/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.41 % (21871)------------------------------
% 0.21/0.41 % (21871)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.41 % (21871)Termination reason: Refutation
% 0.21/0.41
% 0.21/0.41 % (21871)Memory used [KB]: 1173
% 0.21/0.41 % (21871)Time elapsed: 0.024 s
% 0.21/0.41 % (21871)Instructions burned: 37 (million)
% 0.21/0.41 % (21871)------------------------------
% 0.21/0.41 % (21871)------------------------------
% 0.21/0.41 % (21866)Success in time 0.029 s
%------------------------------------------------------------------------------