TSTP Solution File: REL046+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : REL046+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 : n007.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 08:53:11 EDT 2024
% Result : Theorem 0.16s 0.38s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 60
% Syntax : Number of formulae : 181 ( 43 unt; 0 def)
% Number of atoms : 402 ( 148 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 395 ( 174 ~; 167 |; 6 &)
% ( 45 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 47 ( 45 usr; 46 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 214 ( 208 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1113,plain,
$false,
inference(avatar_sat_refutation,[],[f44,f49,f53,f57,f61,f65,f69,f75,f80,f84,f96,f100,f112,f130,f134,f162,f188,f196,f201,f210,f228,f232,f236,f240,f244,f249,f253,f257,f261,f464,f468,f472,f476,f674,f679,f683,f737,f741,f745,f749,f860,f864,f868,f872,f876,f1112]) ).
fof(f1112,plain,
( spl3_2
| ~ spl3_18
| ~ spl3_43 ),
inference(avatar_split_clause,[],[f1019,f866,f186,f41]) ).
fof(f41,plain,
( spl3_2
<=> sK2 = join(sK0,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f186,plain,
( spl3_18
<=> ! [X0] : join(complement(join(complement(sK1),complement(sK2))),X0) = join(sK0,join(complement(join(complement(sK1),complement(sK2))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
fof(f866,plain,
( spl3_43
<=> ! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(join(complement(X0),X1))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_43])]) ).
fof(f1019,plain,
( sK2 = join(sK0,sK2)
| ~ spl3_18
| ~ spl3_43 ),
inference(superposition,[],[f187,f867]) ).
fof(f867,plain,
( ! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(join(complement(X0),X1))) = X0
| ~ spl3_43 ),
inference(avatar_component_clause,[],[f866]) ).
fof(f187,plain,
( ! [X0] : join(complement(join(complement(sK1),complement(sK2))),X0) = join(sK0,join(complement(join(complement(sK1),complement(sK2))),X0))
| ~ spl3_18 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f876,plain,
( spl3_45
| ~ spl3_7
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f173,f160,f63,f874]) ).
fof(f874,plain,
( spl3_45
<=> ! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_45])]) ).
fof(f63,plain,
( spl3_7
<=> ! [X0,X1] : join(X0,X1) = join(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f160,plain,
( spl3_17
<=> ! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
fof(f173,plain,
( ! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0
| ~ spl3_7
| ~ spl3_17 ),
inference(superposition,[],[f161,f64]) ).
fof(f64,plain,
( ! [X0,X1] : join(X0,X1) = join(X1,X0)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f161,plain,
( ! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f872,plain,
( spl3_44
| ~ spl3_7
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f169,f160,f63,f870]) ).
fof(f870,plain,
( spl3_44
<=> ! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(X1,complement(X0)))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_44])]) ).
fof(f169,plain,
( ! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(X1,complement(X0)))) = X0
| ~ spl3_7
| ~ spl3_17 ),
inference(superposition,[],[f161,f64]) ).
fof(f868,plain,
( spl3_43
| ~ spl3_7
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f166,f160,f63,f866]) ).
fof(f166,plain,
( ! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(join(complement(X0),X1))) = X0
| ~ spl3_7
| ~ spl3_17 ),
inference(superposition,[],[f161,f64]) ).
fof(f864,plain,
( spl3_42
| ~ spl3_11
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f118,f98,f82,f862]) ).
fof(f862,plain,
( spl3_42
<=> ! [X2,X0,X1] : join(converse(X0),join(converse(X1),X2)) = join(converse(join(X0,X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_42])]) ).
fof(f82,plain,
( spl3_11
<=> ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
fof(f98,plain,
( spl3_13
<=> ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f118,plain,
( ! [X2,X0,X1] : join(converse(X0),join(converse(X1),X2)) = join(converse(join(X0,X1)),X2)
| ~ spl3_11
| ~ spl3_13 ),
inference(superposition,[],[f99,f83]) ).
fof(f83,plain,
( ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1))
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f99,plain,
( ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2)
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f860,plain,
( spl3_41
| ~ spl3_10
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f102,f94,f78,f858]) ).
fof(f858,plain,
( spl3_41
<=> ! [X2,X0,X1] : composition(converse(X0),composition(converse(X1),X2)) = composition(converse(composition(X1,X0)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_41])]) ).
fof(f78,plain,
( spl3_10
<=> ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f94,plain,
( spl3_12
<=> ! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f102,plain,
( ! [X2,X0,X1] : composition(converse(X0),composition(converse(X1),X2)) = composition(converse(composition(X1,X0)),X2)
| ~ spl3_10
| ~ spl3_12 ),
inference(superposition,[],[f95,f79]) ).
fof(f79,plain,
( ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0))
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f95,plain,
( ! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f749,plain,
( spl3_40
| ~ spl3_7
| ~ spl3_9
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f179,f160,f72,f63,f747]) ).
fof(f747,plain,
( spl3_40
<=> ! [X0] : join(complement(join(zero,complement(X0))),complement(join(top,complement(X0)))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_40])]) ).
fof(f72,plain,
( spl3_9
<=> zero = complement(top) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f179,plain,
( ! [X0] : join(complement(join(zero,complement(X0))),complement(join(top,complement(X0)))) = X0
| ~ spl3_7
| ~ spl3_9
| ~ spl3_17 ),
inference(forward_demodulation,[],[f178,f64]) ).
fof(f178,plain,
( ! [X0] : join(complement(join(complement(X0),zero)),complement(join(top,complement(X0)))) = X0
| ~ spl3_7
| ~ spl3_9
| ~ spl3_17 ),
inference(forward_demodulation,[],[f163,f64]) ).
fof(f163,plain,
( ! [X0] : join(complement(join(complement(X0),zero)),complement(join(complement(X0),top))) = X0
| ~ spl3_9
| ~ spl3_17 ),
inference(superposition,[],[f161,f74]) ).
fof(f74,plain,
( zero = complement(top)
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f745,plain,
( spl3_39
| ~ spl3_7
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f152,f132,f63,f743]) ).
fof(f743,plain,
( spl3_39
<=> ! [X2,X0,X1] : composition(join(X0,X2),X1) = join(composition(X2,X1),composition(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_39])]) ).
fof(f132,plain,
( spl3_16
<=> ! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f152,plain,
( ! [X2,X0,X1] : composition(join(X0,X2),X1) = join(composition(X2,X1),composition(X0,X1))
| ~ spl3_7
| ~ spl3_16 ),
inference(superposition,[],[f133,f64]) ).
fof(f133,plain,
( ! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f741,plain,
( spl3_38
| ~ spl3_7
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f140,f128,f63,f739]) ).
fof(f739,plain,
( spl3_38
<=> ! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_38])]) ).
fof(f128,plain,
( spl3_15
<=> ! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
fof(f140,plain,
( ! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1))))
| ~ spl3_7
| ~ spl3_15 ),
inference(superposition,[],[f129,f64]) ).
fof(f129,plain,
( ! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f737,plain,
( spl3_37
| ~ spl3_4
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f135,f128,f51,f735]) ).
fof(f735,plain,
( spl3_37
<=> ! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).
fof(f51,plain,
( spl3_4
<=> ! [X0] : converse(converse(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f135,plain,
( ! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1))
| ~ spl3_4
| ~ spl3_15 ),
inference(superposition,[],[f129,f52]) ).
fof(f52,plain,
( ! [X0] : converse(converse(X0)) = X0
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f683,plain,
( spl3_36
| ~ spl3_6
| ~ spl3_9
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f184,f160,f72,f59,f681]) ).
fof(f681,plain,
( spl3_36
<=> ! [X0] : join(complement(join(complement(X0),complement(complement(complement(X0))))),zero) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).
fof(f59,plain,
( spl3_6
<=> ! [X0] : top = join(X0,complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f184,plain,
( ! [X0] : join(complement(join(complement(X0),complement(complement(complement(X0))))),zero) = X0
| ~ spl3_6
| ~ spl3_9
| ~ spl3_17 ),
inference(forward_demodulation,[],[f172,f74]) ).
fof(f172,plain,
( ! [X0] : join(complement(join(complement(X0),complement(complement(complement(X0))))),complement(top)) = X0
| ~ spl3_6
| ~ spl3_17 ),
inference(superposition,[],[f161,f60]) ).
fof(f60,plain,
( ! [X0] : top = join(X0,complement(X0))
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f679,plain,
( spl3_35
| ~ spl3_7
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f450,f246,f63,f676]) ).
fof(f676,plain,
( spl3_35
<=> top = join(top,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_35])]) ).
fof(f246,plain,
( spl3_26
<=> top = join(sK0,top) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
fof(f450,plain,
( top = join(top,sK0)
| ~ spl3_7
| ~ spl3_26 ),
inference(superposition,[],[f248,f64]) ).
fof(f248,plain,
( top = join(sK0,top)
| ~ spl3_26 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f674,plain,
( spl3_34
| ~ spl3_9
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f168,f160,f72,f672]) ).
fof(f672,plain,
( spl3_34
<=> ! [X0] : top = join(complement(join(zero,complement(X0))),complement(join(zero,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).
fof(f168,plain,
( ! [X0] : top = join(complement(join(zero,complement(X0))),complement(join(zero,X0)))
| ~ spl3_9
| ~ spl3_17 ),
inference(superposition,[],[f161,f74]) ).
fof(f476,plain,
( spl3_33
| ~ spl3_9
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f139,f128,f72,f474]) ).
fof(f474,plain,
( spl3_33
<=> ! [X0] : zero = join(composition(converse(X0),complement(composition(X0,top))),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).
fof(f139,plain,
( ! [X0] : zero = join(composition(converse(X0),complement(composition(X0,top))),zero)
| ~ spl3_9
| ~ spl3_15 ),
inference(superposition,[],[f129,f74]) ).
fof(f472,plain,
( spl3_32
| ~ spl3_5
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f136,f128,f55,f470]) ).
fof(f470,plain,
( spl3_32
<=> ! [X0] : complement(one) = join(composition(converse(X0),complement(X0)),complement(one)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).
fof(f55,plain,
( spl3_5
<=> ! [X0] : composition(X0,one) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f136,plain,
( ! [X0] : complement(one) = join(composition(converse(X0),complement(X0)),complement(one))
| ~ spl3_5
| ~ spl3_15 ),
inference(superposition,[],[f129,f56]) ).
fof(f56,plain,
( ! [X0] : composition(X0,one) = X0
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f468,plain,
( spl3_31
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f119,f98,f63,f466]) ).
fof(f466,plain,
( spl3_31
<=> ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).
fof(f119,plain,
( ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1))
| ~ spl3_7
| ~ spl3_13 ),
inference(superposition,[],[f99,f64]) ).
fof(f464,plain,
( spl3_30
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f113,f98,f63,f462]) ).
fof(f462,plain,
( spl3_30
<=> ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X1,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).
fof(f113,plain,
( ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X1,X0),X2)
| ~ spl3_7
| ~ spl3_13 ),
inference(superposition,[],[f99,f64]) ).
fof(f261,plain,
( spl3_29
| ~ spl3_6
| ~ spl3_9
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f182,f160,f72,f59,f259]) ).
fof(f259,plain,
( spl3_29
<=> ! [X0] : join(zero,complement(join(complement(X0),complement(X0)))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).
fof(f182,plain,
( ! [X0] : join(zero,complement(join(complement(X0),complement(X0)))) = X0
| ~ spl3_6
| ~ spl3_9
| ~ spl3_17 ),
inference(forward_demodulation,[],[f165,f74]) ).
fof(f165,plain,
( ! [X0] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0
| ~ spl3_6
| ~ spl3_17 ),
inference(superposition,[],[f161,f60]) ).
fof(f257,plain,
( spl3_28
| ~ spl3_6
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f121,f98,f59,f255]) ).
fof(f255,plain,
( spl3_28
<=> ! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).
fof(f121,plain,
( ! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1))))
| ~ spl3_6
| ~ spl3_13 ),
inference(superposition,[],[f99,f60]) ).
fof(f253,plain,
( spl3_27
| ~ spl3_6
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f117,f98,f59,f251]) ).
fof(f251,plain,
( spl3_27
<=> ! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).
fof(f117,plain,
( ! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1)
| ~ spl3_6
| ~ spl3_13 ),
inference(superposition,[],[f99,f60]) ).
fof(f249,plain,
( spl3_26
| ~ spl3_6
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f192,f186,f59,f246]) ).
fof(f192,plain,
( top = join(sK0,top)
| ~ spl3_6
| ~ spl3_18 ),
inference(superposition,[],[f187,f60]) ).
fof(f244,plain,
( spl3_25
| ~ spl3_7
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f89,f82,f63,f242]) ).
fof(f242,plain,
( spl3_25
<=> ! [X0,X1] : converse(join(X0,X1)) = join(converse(X1),converse(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
fof(f89,plain,
( ! [X0,X1] : converse(join(X0,X1)) = join(converse(X1),converse(X0))
| ~ spl3_7
| ~ spl3_11 ),
inference(superposition,[],[f83,f64]) ).
fof(f240,plain,
( spl3_24
| ~ spl3_4
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f88,f82,f51,f238]) ).
fof(f238,plain,
( spl3_24
<=> ! [X0,X1] : converse(join(X1,converse(X0))) = join(converse(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
fof(f88,plain,
( ! [X0,X1] : converse(join(X1,converse(X0))) = join(converse(X1),X0)
| ~ spl3_4
| ~ spl3_11 ),
inference(superposition,[],[f83,f52]) ).
fof(f236,plain,
( spl3_23
| ~ spl3_4
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f87,f82,f51,f234]) ).
fof(f234,plain,
( spl3_23
<=> ! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
fof(f87,plain,
( ! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1))
| ~ spl3_4
| ~ spl3_11 ),
inference(superposition,[],[f83,f52]) ).
fof(f232,plain,
( spl3_22
| ~ spl3_4
| ~ spl3_10 ),
inference(avatar_split_clause,[],[f86,f78,f51,f230]) ).
fof(f230,plain,
( spl3_22
<=> ! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
fof(f86,plain,
( ! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0)
| ~ spl3_4
| ~ spl3_10 ),
inference(superposition,[],[f79,f52]) ).
fof(f228,plain,
( spl3_21
| ~ spl3_4
| ~ spl3_10 ),
inference(avatar_split_clause,[],[f85,f78,f51,f226]) ).
fof(f226,plain,
( spl3_21
<=> ! [X0,X1] : converse(composition(X1,converse(X0))) = composition(X0,converse(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
fof(f85,plain,
( ! [X0,X1] : converse(composition(X1,converse(X0))) = composition(X0,converse(X1))
| ~ spl3_4
| ~ spl3_10 ),
inference(superposition,[],[f79,f52]) ).
fof(f210,plain,
( spl3_20
| ~ spl3_5
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f101,f94,f55,f208]) ).
fof(f208,plain,
( spl3_20
<=> ! [X0,X1] : composition(X0,X1) = composition(X0,composition(one,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
fof(f101,plain,
( ! [X0,X1] : composition(X0,X1) = composition(X0,composition(one,X1))
| ~ spl3_5
| ~ spl3_12 ),
inference(superposition,[],[f95,f56]) ).
fof(f201,plain,
( spl3_19
| ~ spl3_1
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f197,f98,f37,f199]) ).
fof(f199,plain,
( spl3_19
<=> ! [X0] : join(sK1,X0) = join(sK0,join(sK1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
fof(f37,plain,
( spl3_1
<=> sK1 = join(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f197,plain,
( ! [X0] : join(sK1,X0) = join(sK0,join(sK1,X0))
| ~ spl3_1
| ~ spl3_13 ),
inference(superposition,[],[f99,f38]) ).
fof(f38,plain,
( sK1 = join(sK0,sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f196,plain,
( spl3_1
| ~ spl3_17
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f191,f186,f160,f37]) ).
fof(f191,plain,
( sK1 = join(sK0,sK1)
| ~ spl3_17
| ~ spl3_18 ),
inference(superposition,[],[f187,f161]) ).
fof(f188,plain,
( spl3_18
| ~ spl3_3
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f116,f98,f46,f186]) ).
fof(f46,plain,
( spl3_3
<=> complement(join(complement(sK1),complement(sK2))) = join(sK0,complement(join(complement(sK1),complement(sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f116,plain,
( ! [X0] : join(complement(join(complement(sK1),complement(sK2))),X0) = join(sK0,join(complement(join(complement(sK1),complement(sK2))),X0))
| ~ spl3_3
| ~ spl3_13 ),
inference(superposition,[],[f99,f48]) ).
fof(f48,plain,
( complement(join(complement(sK1),complement(sK2))) = join(sK0,complement(join(complement(sK1),complement(sK2))))
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f162,plain,
spl3_17,
inference(avatar_split_clause,[],[f30,f160]) ).
fof(f30,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(f134,plain,
spl3_16,
inference(avatar_split_clause,[],[f33,f132]) ).
fof(f33,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f130,plain,
spl3_15,
inference(avatar_split_clause,[],[f29,f128]) ).
fof(f29,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f112,plain,
( spl3_14
| ~ spl3_6
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f76,f72,f59,f109]) ).
fof(f109,plain,
( spl3_14
<=> top = join(top,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f76,plain,
( top = join(top,zero)
| ~ spl3_6
| ~ spl3_9 ),
inference(superposition,[],[f60,f74]) ).
fof(f100,plain,
spl3_13,
inference(avatar_split_clause,[],[f32,f98]) ).
fof(f32,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(f96,plain,
spl3_12,
inference(avatar_split_clause,[],[f31,f94]) ).
fof(f31,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
fof(f84,plain,
spl3_11,
inference(avatar_split_clause,[],[f27,f82]) ).
fof(f27,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
fof(f80,plain,
spl3_10,
inference(avatar_split_clause,[],[f26,f78]) ).
fof(f26,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f75,plain,
( spl3_9
| ~ spl3_6
| ~ spl3_8 ),
inference(avatar_split_clause,[],[f70,f67,f59,f72]) ).
fof(f67,plain,
( spl3_8
<=> ! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f70,plain,
( zero = complement(top)
| ~ spl3_6
| ~ spl3_8 ),
inference(forward_demodulation,[],[f68,f60]) ).
fof(f68,plain,
( ! [X0] : zero = complement(join(complement(X0),complement(complement(X0))))
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f69,plain,
spl3_8,
inference(avatar_split_clause,[],[f35,f67]) ).
fof(f35,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f23,f28]) ).
fof(f28,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f23,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
fof(f65,plain,
spl3_7,
inference(avatar_split_clause,[],[f25,f63]) ).
fof(f25,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f61,plain,
spl3_6,
inference(avatar_split_clause,[],[f24,f59]) ).
fof(f24,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
fof(f57,plain,
spl3_5,
inference(avatar_split_clause,[],[f22,f55]) ).
fof(f22,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
fof(f53,plain,
spl3_4,
inference(avatar_split_clause,[],[f21,f51]) ).
fof(f21,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f49,plain,
spl3_3,
inference(avatar_split_clause,[],[f34,f46]) ).
fof(f34,plain,
complement(join(complement(sK1),complement(sK2))) = join(sK0,complement(join(complement(sK1),complement(sK2)))),
inference(definition_unfolding,[],[f19,f28,f28]) ).
fof(f19,plain,
meet(sK1,sK2) = join(sK0,meet(sK1,sK2)),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( ( sK2 != join(sK0,sK2)
| sK1 != join(sK0,sK1) )
& meet(sK1,sK2) = join(sK0,meet(sK1,sK2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f17]) ).
fof(f17,plain,
( ? [X0,X1,X2] :
( ( join(X0,X2) != X2
| join(X0,X1) != X1 )
& meet(X1,X2) = join(X0,meet(X1,X2)) )
=> ( ( sK2 != join(sK0,sK2)
| sK1 != join(sK0,sK1) )
& meet(sK1,sK2) = join(sK0,meet(sK1,sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ( join(X0,X2) != X2
| join(X0,X1) != X1 )
& meet(X1,X2) = join(X0,meet(X1,X2)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] :
( meet(X1,X2) = join(X0,meet(X1,X2))
=> ( join(X0,X2) = X2
& join(X0,X1) = X1 ) ),
inference(negated_conjecture,[],[f14]) ).
fof(f14,conjecture,
! [X0,X1,X2] :
( meet(X1,X2) = join(X0,meet(X1,X2))
=> ( join(X0,X2) = X2
& join(X0,X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f44,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f20,f41,f37]) ).
fof(f20,plain,
( sK2 != join(sK0,sK2)
| sK1 != join(sK0,sK1) ),
inference(cnf_transformation,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : REL046+1 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 15:36:22 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % (6471)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.33 % (6474)WARNING: value z3 for option sas not known
% 0.10/0.33 % (6472)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.33 % (6473)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.33 % (6475)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.33 % (6476)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)
% 0.10/0.33 % (6474)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)
% 0.10/0.33 % (6477)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)
% 0.10/0.33 % (6478)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)
% 0.10/0.33 TRYING [1]
% 0.10/0.33 TRYING [2]
% 0.10/0.34 TRYING [3]
% 0.10/0.34 TRYING [1]
% 0.10/0.34 TRYING [2]
% 0.16/0.35 TRYING [3]
% 0.16/0.35 TRYING [4]
% 0.16/0.37 % (6476)First to succeed.
% 0.16/0.38 % (6476)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-6471"
% 0.16/0.38 % (6476)Refutation found. Thanks to Tanya!
% 0.16/0.38 % SZS status Theorem for theBenchmark
% 0.16/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.38 % (6476)------------------------------
% 0.16/0.38 % (6476)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.38 % (6476)Termination reason: Refutation
% 0.16/0.38
% 0.16/0.38 % (6476)Memory used [KB]: 1606
% 0.16/0.38 % (6476)Time elapsed: 0.046 s
% 0.16/0.38 % (6476)Instructions burned: 87 (million)
% 0.16/0.38 % (6471)Success in time 0.061 s
%------------------------------------------------------------------------------